S. L. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proc. of the ACM SIGMOD Conf. on Management of Data, pages 158--167, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....used as such a mechanism to specify and investigate most of the natural sequence operations. Sequence operations in database query languages tend to be high level in nature (in contrast to those in programming languages such as C, Lisp and Prolog) For example, in the EXCESS algebra of EXODUS [17], HEAD and SUBARRAY are employed to obtain the head and a subinterval of a sequence, respectively. Such operations specify results of processes rather than the processes themselves. The specification of the results of such high level sequence operations can be viewed as a type of pattern ....

S. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proceedings of the 1991.

....coherence and consistency. Fifth, we allow for interval probabilities over solution sets of temporal constraints, while their work allows only for precise point probabilities over intervals of time points. Our work is also related to data models and algebraic operations for complex objects [1, 37, 44, 41, 40, 6]. Our work is a strict extension of the algebra for complex values presented by Abiteboul et al. 1] As in the case of Shaw and Zdonik [37] Vandenberg and DeWitt [44] and Boncz et al. 6] our data model supports the type constructors for sets and tuples on elementary datatypes. Like them, we ....

....intervals of time points. Our work is also related to data models and algebraic operations for complex objects [1, 37, 44, 41, 40, 6] Our work is a strict extension of the algebra for complex values presented by Abiteboul et al. 1] As in the case of Shaw and Zdonik [37] Vandenberg and DeWitt [44], and Boncz et al. 6] our data model supports the type constructors for sets and tuples on elementary datatypes. Like them, we also support the algebraic operations of selection, projection, join, union, intersection, and difference. However, unlike them, we do not support the type constructors ....

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S. L. Vandenberg and D. J. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proceedings SIGMOD-91, pages 158--167. ACM Press, 1991.

....[20] 25] 28] as well as Knowledge Base Management Systems (KBMS) 3] 24] 30] feature an object oriented knowledge model and an associated query language. In analogy to conventional database systems (DBMS) both types of systems can employ an algebraic approach for query processing [5] 31] [33], furthermore called knowledge processing. In this approach, a query is firstly mapped into an algebraic representation, which is then successively rewritten and transformed into an execution plan consisting of plan operators, before it is actually performed. An adequate concept for query ....

Vandenberg, S.L., DeWitt, D.J.: Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance, Proc. ACM SIGMOD Int. Conf. on Management of Data, Denver, Colorado, 1991, 158-167.

....increasingly clear that query processing in extensible and object oriented systems will also be based on algebraic techniques, i.e. by defining algebra operators, algebraic equivalence laws, and suitable implementation algorithms. Several object oriented algebras have recently been proposed, e.g. [ShZ90, StO91, VaD91] among manyothers. Their common thread is that algebra operators consume one or more bulk types (e.g. a set, bag, array,time series, or list) and produce another one suitable as input into the next operator.The execution engines for these systems are also based on algebra operators, i.e. ....

....optimizer a complex and tedious task. Vo lcano salgebraic approach seems much more natural and easier to understand. Most recent work in object oriented query optimization and some work on database programming languages has focused on algebras and algebraic transformations, e.g. [LiD92, ShZ90, StO91, VaD91] among manyothers. Second, in order to avoid the problems associated with adding newoperators to the costbased optimizer,new operators are integrated at the query rewrite level. However, query optimization on the query rewrite levelisheuristic; in other words, it does not include cost estimation. ....

S. L. Vandenbergand D. J. DeWitt, Algebraic Support for ComplexObjects with Arrays, Identity,and Inheritance, Proc. ACM SIGMOD Conf.,Denver, CO, May 1991, 158.

.... Server . 4. 3 Optimization Rule based transformation and optimization of operator graphs have been studied for more than a decade in the context of extendible database query optimizers [RH87, CZ96] optimizer generators [SS90, GM93] and query optimizers for object oriented databases [VD91]. Structurally, filter graphs are nearly identical to operator graphs. Semantically, of course, they are different there exist, however, several analogies: Logic operators (e.g. join) correspond to virtual filters, while the implementations of logic operators (physical operators, e.g. ....

.... 21 SFB 501 A3 Related Work the implementation must be deduced from the data type at run time ( virtuality of our filters, however, is not stemming from explicit type inheritance, but from a deducible media type affinity) Algebraic support for types with virtual methods is described, e.g. in [VD91]. Consequently, the structural and (from an abstract point of view) also semantic similarity of operator and filter graphs additionally motivates our algebraic approach for realizing filter graph transformation and optimization, since such an approach would mostly benefit from the vast amount of ....

Vandenberg, S. L., DeWitt, D. J.: Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. In: Proc. of the 1991 ACM SIGMOD Int. Conf. on Management of Data (Denver, Colorado, May 29--31), SIGMOD Record Vol. 20, Issue 2, June 1991, pp.158--167.

....Database the applicable constraints being compiled and associated within appropriate object types. Finally, contributions and open research issues are addressed in Section 6. 1. 1 Motivating Examples Consider an object oriented database schema, using the generic notation of EXTRA EXCESS [17], and IQL [1] where attributes are defined as a pair attribute: domain and constraints are associated with an object type. Consider an example shown in Figure 1 consisting projects (Proj) defense projects (DefProj) which are specializations of projects, and technical managers (TechMgr) who ....

Scott L. Vandenberg and David J. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In James Clifford and Roger King, editors, Proc. ACM SIGMOD Intl. Conf. on Management of Data, pages 158--167, Denver, CO, 1991.

....conditions, access nested structure, or produce nested results, an essential feature found in these languages is the nesting of queries, i.e. the embedding of a query into another query. The optimization of object oriented (oo) queries has been intensively studied using algebraic rewriting [4, 7, 23, 24, 25] or rewriting of path expressions [7, 13, 14] However, in spite of the importance of nested queries, we do not know of any research on their optimization. Nested queries in the oo context are usually translated into nested algebraic expressions which are evaluated through rather inefficient ....

S. L. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proc. of the ACM SIGMOD Conf. on Management of Data, pages 158--167, 1991.

....reasons for designing algebras for data models is to use them as vehicles for query optimisation in systems supporting high level interfaces such as query languages. A large number of algebras have been proposed for data models richer than the relational model [Osb88, Day89, CDLR89, SZ89, SO90, VD90, DD91, WT91, Van92, Alh92, Nor92, AB93, Mit93, GM93, LW93] Many of these algebras extend the relational algebra to manipulate richer modelling constructs and object identifiers as well as to provide more expressive and computational powers. Others take a fundamentally different approach and draw ....

....and link to the source are essential. Straube s algebra [Str90] cannot generate new objects and does not maintain source links. Dayal s algebra [Day89] and Shaw Zdonik s algebra [SZ90] rely on tuples and keep no source links. Osborn s algebra [Osb88] and Vandenberg DeWitt s algebra [VD90] does not maintain source links. It was mentioned earlier that views can be used to restructure information. To support that using a query driven approach requires a powerful query language. As expressive power has been covered briefly in previous chapters, the centre of the following discussion ....

S.L. Vandenberg and D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Technical Report 987, University of Wisconsin - Madison, U.S.A., December 1990.

.... that can occur over database objects (e.g. only those actions that can be specified with a non complete query language are permitted) Object oriented database research, on the other hand, has attempted to introduce notions of inheritance, subtyping, and object identity to database systems (e.g. [3, 36, 37, 7, 26, 60, 58]) These systems are showing promise, but they have a number of shortcomings. First, they tend to be computationally restricted to enable query optimization; those that do not have this restriction usually overcome it by embedding the objectoriented database in a host language, which causes ....

....varying length arrays using other types. Object oriented databases often provide array constructors (e.g. 3, 60] but these are generally limited in the same ways that programming language arrays are (two notable exceptions are Gemstone [33] which provides an indexed set class, and EXTRA [58], which provides an explicit varying length array constructor that does not support insertion but that does support tail expansion) Finally, support for relations and relationships is highly variable among existing systems. Relational databases do, of course, support both types of objects. The ....

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S.L. Vandenberg and D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. In Proceedings of the 1991 ACM SIGMOD International Conference on Management of Data, pages 158-- 167, May 1991.

....that the database is in fact in a consistent state after the execution of the application code. Support from existing databases is mostly in the form of a built in pre de ned set of consistency de nitions, such as referential integrity [MS90] programming language kinds of consistency de nitions [VD91, AH90] such as assertions and exception handling mechanism in languages like C , Java, Ada, or domain constraints over only a subset of types such as constraints on collection types [SHO95] Relational database systems (RDBs) o er some control over constraint speci cation by users via the ....

....in applying formal veri cation as a technique for maintaining the consistency of the database during schema evolution as done by our work. Consistency Management. Support from ODBMS mostly follows the support that is already provided by programming languages in terms of consistency de nitions [VD91, AH90] such as assertions and exception handling mechanisms in languages like C , Java and Ada. Relational database systems (RDBMS) o er some additional support in the form of triggers but only support roll back semantics, i.e. if a constraint is not satis ed at the end of a transaction, then ....

S.L. Vandenberg and D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity and Inheritance. In SIGMOD, pages 158-167, 1991. 16 A Taxonomy of Schema Evolution Operations We also present here the contract-serf templates for each of the primitives specied in

....We also expect it to incorporate object identity and the ability to operate on user defined types through messages. There have been numerous proposals for object algebras, such as those of Beeri and Kornatsky [8] and Osborn [9] We expect that ours will resemble those of Vance [10] and Vandenberg [11]. It might seem, then, that specifying the parser optimizer interface is a matter of selecting a semantic formalism, such as set theory, equational specifications or denotational semantics, and giving a definition to each operator in the algebra. However, from the point of view of the optimizer ....

Vandenberg, SL and DeWitt, DJ. Algebraic support for complex objects with arrays, identity and inheritance. Proc. 1991 ACM SIGMOD Intl. Conf. on Management of Data:158-167, Denver, May 1991.

....semantically equivalent filter graphs. Rule based transformation and optimization of operator graphs have been studied for more than a decade in the context of extendible database query optimizers [RH87, CZ96] optimizer generators [SS90, GM93] and query optimizers for object oriented databases [VD91]. Structurally, filter graphs are nearly identical to operator graphs. Semantically, of course, they are different there exist, however, several analogies: Logic operators (e.g. join) correspond to virtual filters, while the implementations of logic operators (physical operators, e.g. ....

.... applied to, in a sense that the implementation must be deduced from the data type at run time ( virtuality of filters, however, does not come from explicit type inheritance, but from an implicitly assumed type affinity) Algebraic support for types with virtual methods is described, e.g. in [VD91]. Consequently, the structural and (from an abstract point of view) also semantic similarity of operator and filter graphs gives reason to follow an algebraic approach for realizing filter graph transformation and optimization. Such an approach would mostly benefit from the vast amount of ....

Vandenberg, S. L., DeWitt, D. J.: Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. In: Proc. of the 1991 ACM SIGMOD Int. Conf. on Management of Data (Denver, Colorado, May 29--31), SIGMOD Record Vol. 20, Issue 2, June 1991, pp. 158--167.

....system, because there are a number of different ways to express a join in such systems. In this thesis, we ignore the optimization of joins written in a non procedural fashion. They can be optimized using standard relational techniques [SELI79] or the more complex techniques developed for OODBSs [SHAW89, BEER90, VAND91]. Instead, we will concentrate on set iterators. Since DBPLs such as PASCAL R [SCHM77] O 2 [LECL89] E [RICH92] and O [AGRA89] provide constructs to iterate through a set in some unspecified order, it is possible to nest iterators to express value based joins. The following is an example of a ....

Scott Vandenberg and David DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Proc. 1991 SIGMOD, May 1991.

....also more powerful because it can express duplicate elimination, manipulate lists, handle inheritance trees. IQL is more powerful than languages in [5, 14] User level query laguages such as EXCESS [8] and [2] are can be seen as sublanguages of OQL. Shaw and Zdonik [19] and Vadenberg and DeWitt [21] provide object algebra for object oriented databases. But neither of them attempt to manipulate mixture of sets and lists. A few other languages attempt to incorporate objectoriented features into logic programs. But that is not the goal of OQL. OQL uses the logic programming paradigm simply to ....

S. L. Vandenberg, and D. J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Proc. of ACM SIGMOD Conf., 1991.

....from other algebras in its provision of operations specific to binary collections (relationships) Andersen [And91] Scholl et al. [SST92] Shaw and Zdonik [SZ89] SZ90] and Straube [Str90] all restrict their attention to set collections. Both Cluet et al. [CDLR90] and Vandenberg and DeWitt [VD91] cater for multiple kinds of collections. Arising from the two forms of collections unary and binary the collection algebra has two groups of operations. Any operation that can be applied to unary collections can also be applied to binary collections by regarding the pairs belonging to that ....

S. L. Vandenberg and D. J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. In Proceedings of SIGMOD 91, 1991.

.... example is genome databases, in which long sequences representing genetic information are stored, and sophisticated pattern matching and restructuring facilities are needed [11] These new applications have led to the introduction of sequence types in recent data models and query languages (e.g. [2, 4, 5, 28]) In many cases, however, queries over sequences are described only by means of a set of pre defined, ad hoc operators, and are not investigated in a theoretical framework. In other cases, e.g. 19, 25] query languages concentrate on pattern extraction capabilities and do not consider sequence ....

S. Vandenberg and D. De Witt. Algebraic support for complex objects with arrays, identity and inheritance. In ACM SIGMOD International Conf. on Management of Data, 1991.

....an object oriented database, and (ii) employing the relationships between the individual objects and the conceptual schema in conventional queries. 1. 2 Querying Nested Components of Complex Objects There are two main approaches to the manipulation of complex objects used by recent object algebras [54, 2, 47, 32, 33, 51]. The first approach evolved from the nested relational algebras [41, 1] The operations used in this approach include variants of the NF 2 operations nest and unnest [41] together with operations for creating and flattening a set of sets [47] This approach is used in some recent object ....

S.L. Vandenberg, D.J. DeWitt, Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance, Proc. of the ACM Conf. on Management of Data, 1991, pp. 158-167.

....of databases, a functional language incorporating parametrized set types is introduced. Different kinds of (not necessarily formal) object equality definitions are studied in [Mas89] The implementation of the proposed concepts in the database management system OMEGA is also discussed there. In [VD91] algebraic query processing was the main motivation for given a set theoretic semantics for object identities in the presence of multiple inheritance. The paper also discusses implementation issues in the context of the EXTRA EXCESS system. A similar framework like ours but with emphasis on ....

S.L. Vandenberg and D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. In Proc. ACM SIGMOD Conf. on Management of Data (SIGMOD'91), SIGMOD Record, 20(2), pages 158--167, , 1991.

....a fundamental characteristic of oo query languages. Yet, their optimization has remained largely unexplored. We propose novel techniques for efficiently evaluating nested queries in oo languages. In the last few years, many algebras have been proposed for the optimization of oo query languages [2, 3, 7, 16, 28, 30, 31]. Most of them allow the representation of nested algebraic expressions (e.g. a join may occur within the predicate of a selection) However, the proposed algebraic equivalences do not deal with these nested parts that remain nested throughout the rewriting process. Finally, they are evaluated ....

S. L. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proc. of the ACM SIGMOD Conf. on Management of Data, pages 158--167, 1991.

....which provide general programming capability for type checking and computation of result types in specifications. The GraphDB algebra shows typing and algebraic modeling for a number of graph based concepts which have not yet been captured in object oriented query algebras (e.g. ShZd 90,VaDe 91] for example for path types, description of relevant subgraphs in queries, or generation of link objects in queries. The paper is organized as follows: In Section 2 we introduce the basic concepts of second order signature. Section 3 introduces an SOS specification for the type system of ....

....like the select operator of [St z 90] to compute joins. In this case the on operator is required to combine the operands of the join. The class and linkClass operators generate new objects. These operators are similar to the image and project operators of [ShZd 90] The approach taken in [VaDe 91] is different from [ScSc 90] ShZd 90] St z 90] and our algebra. VaDe 91] define orthogonal type constructors for multiset types, tuple types, arraytypes, and object identifiers. Instead of defining most operators to work on sets of entities they provide operators for each of the four basic ....

[Article contains additional citation context not shown here]

Vandenberg, S.L., and D.J. DeWitt, Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Proc. ACM SIGMOD 1991, 158-167.

....the object algebra should include operations for querying database conceptual schema. A more detailed argument in favor of the stated motivations for the design of the object algebra is given in the following three sections. Finally, we mention that most approaches to the design of object algebras [81, 70, 5, 46, 50, 52, 77] do not agree in the basic operations of the algebra. Therefore, it is also interesting to investigate the common principles of existing object algebras and to define a set of operations that would cover most of the existing approaches. 1.1.1 Database algebras and database programming languages ....

....of data objects to database schema. Next, some aspects of object composition abstraction can be represented using data model constructs. In the pure object oriented database model [9] composite objects are modelled by object identifiers and complex attributes. The EXCESS database model [81] introduces the own and ref constructs for expressing the semantics of composite objects. The ref construct denotes the reference between objects. The own construct can represent the fact that a given component object is actually part of exactly one composite object. It can not be referenced by ....

S.L. Vandenberg, D.J. DeWitt, Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance, ACM SIGMOD 1991

....conditions, access nested structure, or produce nested results, an essential feature found in these languages is the nesting of queries, i.e. the embedding of a query into another query. The optimization of object oriented (oo) queries has been intensively studied using algebraic rewriting [4, 6, 20, 22, 23] or rewriting of path expressions [6, 10, 11] However, in spite of the importance of nested queries, we do not know of any research on their optimization. Nested queries in the oo context are usually translated to nested algebraic expressions which are evaluated through rather inefficient nested ....

S. L. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proc. of the ACM SIGMOD Conf. on Management of Data, pages 158--167, 1991.

....[Gueting, Zicari, and Choy 1989] also proposes a many sorted algebra, thus 20 Chapter 5. Algebraic Query Optimization in CoOMS allowing for the inclusion of operators like count or card. Finally, an algebra similar to our approach has recently been proposed for the EXTRA EXCESS data model [Vandenberg and DeWitt 1991]. An algebra is especially useful to represent queries for optimization and evaluation. Because we consider a structurally object oriented data model, we do not have the problem of optimizating queries including methods. Other algebraic formalisms for structurally object oriented data models have ....

....and evaluation. Because we consider a structurally object oriented data model, we do not have the problem of optimizating queries including methods. Other algebraic formalisms for structurally object oriented data models have been suggested in several projects ( Osborn 1988] Straube 1991] [Vandenberg and DeWitt 1991], Zdonik 1988] 5.6 Conclusion In this paper, we first have presented the structurally object oriented data model NO 2 , including the data definition facilities, a descriptive query language, and an algebraic formalization. As far as algebraic optimization is concerned, rules and ....

S.L. Vandenberg, D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. ACM-SIGMOD Intl. Conf. on Management of Data, 1991.

....interesting to explore the creation of arbitrary new types by the algebraic operations. EQUAL can build objects with new complex types out of parameterized sets and tuples, and other languages build values with new types constructed from their basic types (sets, tuples, lists, arrays) e. g [32] [150]) We would like to explore building new abstract objects in response to queries. For example, if we define an abstract data type D, we would like to write a query that can build new objects of type D. Such a capability might be also be interesting to explore as a way to define views in o o ....

Scott L. Vandenberg and David J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. In SIGMOD Proceedings, pages 158--167. ACM, June 1991.

....functions (relationships) between objects. In the area of query languages for complex object databases, researchers have successfully extended the well known relational query languages. This has resulted in calculus, algebraic, rulebased, and SQL like query languages for complex object databases [1, 2, 3, 31, 35, 53]. In contrast, the study of query languages for function based object databases is less developed. In this area, the most progress has been made in the specification of SQL and rule based languages [5, 9, 28, 39, 47] Although proposals for function based object algebras have appeared in the ....

....developed. In this area, the most progress has been made in the specification of SQL and rule based languages [5, 9, 28, 39, 47] Although proposals for function based object algebras have appeared in the literature, such algebras strongly resemble the algebras defined for complex object databases [13, 18, 46, 53]. Defining algebras in this fashion deviates from the basic philosophy of the pure function based approach as the level of abstraction at which these algebras operate is several layers higher than the graphoriented nature of the function based approach. Given this situation, we propose a simple ....

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S.L. Vandenberg and D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity and Inheritance. In Proc. ACM SIGMOD Int'l Conf. on Management of Data, Denver, Colorado, 1991, pp. 158--167.

.... A number of proposals for object oriented query languages include arrays, see [22, 9] The ODMG proposal includes one dimensional arrays with a limited set of supported operations [8] Vandenberg and DeWitt propose an object oriented algebra supporting arrays in addition to other constructs [31, 30]. They only treat one dimensional arrays. The array operations in [31, 30] are very similar to typical list operations, but also include operations for array subscripting. Organization. In section 2 we describe the design of a nested relational calculus for arrays, NRCA. This calculus forms the ....

....see [22, 9] The ODMG proposal includes one dimensional arrays with a limited set of supported operations [8] Vandenberg and DeWitt propose an object oriented algebra supporting arrays in addition to other constructs [31, 30] They only treat one dimensional arrays. The array operations in [31, 30] are very similar to typical list operations, but also include operations for array subscripting. Organization. In section 2 we describe the design of a nested relational calculus for arrays, NRCA. This calculus forms the theoretical basis for our array query language AQL in much the same way ....

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S. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity and inheritance. In SIGMOD'91, pages 158--167.

....operations for creating, inserting, updating, subscripting and resizing. Their arrays seem to support in place updates, since they can have holes and there is an explicit resize operation. Vandenberg and DeWitt propose an objectoriented algebra supporting arrays in addition to other constructs [31, 32]. They only treat one dimensional arrays. The array operations in [31, 32] are very similar to typical list operations, but also include operations for array subscripting. Organization. In section 2 we describe the design of a nested relational calculus for arrays, NRCA. This calculus forms the ....

....Their arrays seem to support in place updates, since they can have holes and there is an explicit resize operation. Vandenberg and DeWitt propose an objectoriented algebra supporting arrays in addition to other constructs [31, 32] They only treat one dimensional arrays. The array operations in [31, 32] are very similar to typical list operations, but also include operations for array subscripting. Organization. In section 2 we describe the design of a nested relational calculus for arrays, NRCA. This calculus forms the theoretical basis for our array query language AQL in much the same way ....

[Article contains additional citation context not shown here]

S. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity and inheritance. In SIGMOD'91, pages 158--167.

....a transaction, the effects of the transaction are undone. Many database programming languages and objectoriented databases support only a limited, predefined set of consistency definitions, such as referential integrity (e.g. 23] or programming language kinds of consistency definitions (e.g. [37, 1]) or they support consistency definitions over only a subset of types (typically collection types; e.g. 33, 9] Active database systems (e.g. 8, 20, 6] include reactive control primitives, typically in the form of eventcondition action (ECA) rules, that can facilitate consistency ....

S. L. Vandenberg and D. J. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proc. SIGMOD Int'l. Conf. on Management of Data, pages 158--167, May 1991.

.... algebraic form as follows: map(flatten(map(filter(Cities; c: c:name = Portland ) c: join(c:hotels; c:places to visit; h; p) h:name = p:name) h; p) h:name) Even though there are ways of translating SQL like queries over nested sets into NF 2 form (as is done in the SHORE project [21]) these approaches become infeasible when multiple collection types are introduced. First, the number of required algebraic operators increases dramatically. For example, if we had n collection types we would need n 3 different join operators, since we may need to join two different collection ....

S. Vandenberg and D. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Proceedings of the ACM-SIGMOD International Conference on Management of Data, Denver, Colorado, 20(2), May 1991.

....data models. These works can be classified into three categories: 1. formal work which tries to cover the structural part of object oriented databases, e.g. 8, 23] including the specification of algebras most of which have their origins in the work on nested relations (NF 2 ) e.g. [25, 26, 28]; 2. formal, logic programming based models, e.g. 4, 10, 13, 20, 21, 22] and 3. informal work on object oriented databases discussing features a formal model should exhibit, e.g. 9, 24] The major challenge in formalizing object oriented data models stems from the destructive updating nature ....

.... 2 Axp z 1 (L) AE 2 2 Axp z 2 (L) with z i = fz 0 i g, z 0 i 2 TS , where z 0 1 and z 0 2 have no attribute in common, ffl 2 Bxp(L) and x 2 X fz 0 1 ffiz 0 2 g : AE 1 1 x(ffl) AE 2 ) 2 Axp fz 0 1 ffiz 0 2 g (L) There are two casting operations also called dereferences [3, 28] which transform an object described by an OID expression to a value expression. These casting operations are overloaded, i.e. they have the same operator symbol . 13. if z 2 T with j(z) hA 1 : z 1 ; A n : z n i and AE 2 Axp z (L) then (AE) is an element of Axp hA 1 :z 1 ; A n :z ....

S. L. Vandenberg and D. J. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proc. of the ACM SIGMOD Conf. on Management of Data, pages 158--167, Denver, CO, May 1991.

.... Fox adds the disjoint and overlaps operators for comparing two collections (although they may be simulated using set intersection and an (in)equality comparison with the empty set) Collection objects may also be combined with set theoretic union, intersection, and difference, and additive union [VD91] Note that shallow equality for collection objects is the same as a membership test for equality. As an example, the following query finds the input parameters of all experiments using a system that Jo used. for e in Experiment select tuple e.input.wind speed, e.input.humidity, e.input.wind ....

S.L. Vandenberg and D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity and Inheritance. In Proceedings of the ACM SIGMOD International Conference on Management of Data, pages 158--167, Denver, CO, May 1991.

....changes to relations and to SQL [TSQL94] However, it would be interesting to study how time ordered sequences can be efficiently converted into relations with time stamps, and viceversa. While most object oriented database proposals include constructors for complex types like lists and arrays [VD91, BDK92], they can either be treated as collections, or manipulated using a primitive set of methods; no facilities for sequence queries are provided. The work described in [Ric92] is an exception, and proposes an algebra based on temporal logic to ask complex queries over lists. There have also been ....

S.L. Vandenberg and D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. In Proceedings of ACM SIGMOD '91 International Conference on Management of Data, pages 158--167, 1991.

....of a specification framework and shown applications to relational modeling, query processing, updates, and optimization. Future work might include the following: Try to define more complex data models and algebras for queries or query processing within the SOS framework, such as, for example, [AbH84, ShZ89, ScS90, VaD91]. This study should clarify how much can be done with the specification techniques described and which additional techniques are needed. Define the semantics of specifications by mapping them into a second order signature. Implement an SOS parser optimizer. Acknowledgments Initial ideas ....

Vandenberg, S.L., and D.J. DeWitt, Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Proc. ACM SIGMOD 1991, 158-167.

....of databases, a functional language incorporating parametrized set types is introduced. Different kinds of (not necessarily formal) object equality definitions are studied in [Mas90] The implementation of the proposed concepts in the database management system OMEGA is also discussed there. In [VD91] algebraic query processing was the main motivation for given a set theoretic semantics for object identities in the presence of multiple inheritance. The paper also discusses implementation issues in the context of the EXTRA EXCESS system. SSW92] treats Work reported here has been ....

S.L. Vandenberg and D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. SIGMOD Record, 20(2):158--167, 1991. Proc. ACM SIGMOD Conf. on Management of Data (SIGMOD'91).

....of objectoriented databases and their query optimizers. We propose the stack based approach to query languages as an adequate framework aiming at the same goals. 1 Introduction Object algebras are proposed as tools to formalise object oriented databases and their query languages (QLs) see [AbFi95, AlAr93, BaWi94, CDV88, Clue89, ClDe92, ClDe94, DGG94, GZC89, HFLP89, KeMa94, LMSVVZ93, Liu93, PoSm94, ShZd89a, ShZd89b, ShZd90, StOz90, SZLV93, SLVZ95, VaDe91], and many others. They are claimed to be well suited to solve query optimisation problems. In this paper we carry out a critical analysis of this research activity. There are two principal reasons motivating our work. First, we see in these algebras severe flaws, which cause doubts concerning ....

S.L. Vandenberg, D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Proc. of SIGMOD Conf. 1991, pp. 158-167

.... example is genome databases, in which long sequences representing genetic information are stored, and sophisticated pattern matching and restructuring facilities are needed [15] These new applications have led to the introduction of sequence types in recent data models and query languages (e:g: [3, 6, 7, 32, 12]) In many cases, however, queries over sequences are described only by means of a set of pre defined, ad hoc operators, and are not investigated in a theoretical framework. In other cases, e:g: 23, 28] query languages concentrate on pattern extraction capabilities and do not consider sequence ....

S. Vandenberg and D. De Witt. Algebraic support for complex objects with arrays, identity and inheritance. In ACM SIGMOD International Conf. on Management of Data, pages 158--167, 1991.

....are discussed elsewhere in this book. Work on object algebras has been more prevalent. There are many algebras that have been defined with varying operations (e.g. Alhajj 1993; Beeri and Kornatzky 1990; Blakeley et al. 1993; Peters et al. 1993; Shaw and Zdonik 1990; Straube and Ozsu 1990a; Vandenberg and DeWitt 1991]) 2.2 Optimizer Architecture Query optimization can be modeled as an optimization problem whose solution is the choice of the optimum state in a state space (also called search space) In query optimization, each state corresponds to an algebraic query indicating an execution schedule and ....

VANDENBERG, S., ANDDEWITT, D. 1991. Algebraic support for complex objects with arrays, identity, and inheritance.

.... example is genome databases, in which long sequences representing genetic information are stored, and sophisticated pattern matching and restructuring facilities are needed [11] These new applications have led to the introduction of sequence types in recent data models and query languages (e.g. [2, 4, 5, 28]) In many cases, however, queries over sequences are described only by means of a set of predefined, ad hoc operators, and are not investigated in a theoretical framework. In other cases, e.g. 16, 25] query languages concentrate on pattern extraction capabilities and do not consider sequence ....

S. Vandenberg and D. De Witt. Algebraic support for complex objects with arrays, identity and inheritance. In ACM SIGMOD, 1991.

....the potential of object algebras, in the proposed forms, as formal and intellectual tools for the development of objectoriented databases and their query optimizers. 1 Introduction Object algebras are proposed as tools to formalise objectoriented databases and their query languages (QLs) see [AlAr93, BMG93, CDV88, Clue89, ClDe92, ClDe94, DGG94, GZC89, HFLP89, KeMa94, LMSVVZ93, PoSm94, ShZd89a, ShZd89b, ShZd90, StOz90, SZLV93, SLVZ95, VaDe91], and many others. They are claimed to be well suited for query optimization. In this paper we carry out a critical analysis of this research activity. There are two principal reasons motivating our work. First, we see in these algebras severe flaws, which cause doubts concerning their ....

S.L. Vandenberg, D.J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Proc. ACM SIGMOD Conf., 1991, pp.158-167

....constraint box. 5 Related Work In recent years, a considerable number of database models and query languages have been proposed for databases that contain sequential data objects. These models may be broadly classified as follows: 1. Complex object based. In these models [BBKV87, BCD89, GZC89, VD91] the list type constructor is one of many collection based data type constructors. The ODMG object model [Cat94] and the various object relational database models [Sto93, Kim94] incorporate these type constructors. Typically, list algebraic operators are supported which can be incorporated in ....

S. L. Vandenberg and D. J. DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. In J. Clifford and King. R., editors, Proceedings of the 1991 ACM SIGMOD International Conference on Management of Data, pages 158--167, Denver, CO, May 1991. ACM.

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Scott Vandenberg and David DeWitt. Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. Proc. 1991 SIGMOD, May 1991.

....proposals as well as those of other researchers on the topic have explored some of the fundamental issues and provided the starting point for the work reported here. AQUA (A QUery Algebra) is the result of a joint effort among researchers who have participated in the design of previous algebras [26, 30, 31]. AQUA has been designed to address a number of detailed modeling issues that we believe needed further work, but the overarching goal for this work has been the design of an algebra that would serve as the input to a broad class of query optimizers. In this way, it could be used as a de facto ....

....to a point) Other models have claimed similar goals, but not necessarily in all these areas at once, and our mechanisms for achieving these goals differ substantially from those of our predecessors. Many of the specific constructs of AQUA were inspired by or drawn from the EXTRA EXCESS system [31], ENCORE EQUAL [26] and Revelation [30] AQUA is intended to support large numbers of bulk types and to do so in a flexible, uniform way, such that the addition of other bulk types later on will be straightforward. 6] proposes a meta level algebra for collections of complex objects with ....

[Article contains additional citation context not shown here]

S. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In James Clifford and Roger King, editors, Proceedings of the SIGMOD International Conference on Management of Data, pages 158--167, Denver, Colorado, May 1991. 14

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S. L. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proc. of the ACM SIGMOD Conf. on Management of Data, pages 158--167, 1991.

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S. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity and inheritance. In SIGMOD'91, pages 158--167.

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S.L. Vandenberg and DeWitt D.J., \Algebraic Support for Complex Objects with Arrays, Identity and Inheritance," CS-TR-987, University of Wisconsin-Madison, December 1990.

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S.L. Vandenberg and DeWitt D J, Algebraic Support for Complex Objects with Arrays, Identity and Inheritance, in: Proc. of ACM-SIGMOD, 1991.

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S.L. Vandenberg and DeWitt D.J., \Algebraic Support for Complex Objects with Arrays, Identity and Inheritance," Proceedings of the ACM-SIGMOD International Conference on Management of Data, 1991. 20

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S. L. Vandenberg and D. DeWitt. Algebraic support for complex objects with arrays, identity, and inheritance. In Proc. of the ACM SIGMOD Conf. on Management of Data, pages 158--167, 1991.

No context found.

Vandenberg, S., DeWitt, D.: Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance. ACM SIGMOD, 1991.

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VD91 Vandenberg, S.L., DeWitt, D.J.: Algebraic Support for Complex Objects with Arrays, Identity, and Inheritance, J. Clifford, R. King (eds), Proc. ACM SIGMOD, Denver, Colo. SIGMOD Record 20(2), 1991, 158-167.

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