Various models and languages for describing and manipulating hierarchically structured data have been proposed. Algebraic, calculus-based and logic-programming oriented languages have all been considered. This paper presents a general model for complex objects, and languages for it based on the three paradigms. The algebraic language generalizes those presented in the literature; it is shown to be related to the functional style of programming advocated by Backus. The notion of domain independence familiar from relational databases is defined, and syntactic restrictions (referred to as safety conditions) on calculus queries are formulated, that guarantee domain independence. The main results are: The domain-independent calculus, the safe calculus, the algebra, and the logic-programming oriented language have equivalent expressive power. In particular, recursive queries, such as the transitive closure, can be expressed in each of the languages. For this result, the algebra needs the pow...

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 complex-object 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...

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...

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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...

Database systems that can efficiently manage complex objects are increasingly needed in many different fields such as office automation, knowledge processing, CAD/CAM, CASE, etc. A lot of recent complex object database systems support the concepts of object identity and object identifier. Following an object identifier to access the referenced object is called navigation operation and is an essential operation in dealing with complex objects. Navigation operation is a difficult operation to implement efficiently since every navigation operation inherently causes one disk access operation. This paper proposes a scheme to notably accelerate the navigation operation among a sea of complex objects, by increasing the effectivenumber of objects in one disk page. The main concept of the presented technique is threefold: The first is to store a cached value within a complex object that is referencing another complex object. The second is that when the referenced object is to be updated the update propagation is delayed until the time when the cached value is referenced. Lastly, the third idea is to utilize a hashed table on main memory to efficiently validate the consistency between the cached values and the original values. Index terms --- Complex objects, object-oriented database, object identity, persistent objects, caching, and delayed update propagation. I

We present a functional framework for database query languages, which is analogous to the conventional logical framework of first-order and fixpoint formulas over finite structures. We use atomic constants of order 0, equality among these constants, variables, application, lambda abstraction, and let abstraction; all typed using fixed order ( 5) functionalities. In this framework, proposed in [21] for arbitrary order functionalities, queries and databases are both typed lambda terms, evaluation is by reduction, and the main programming technique is list iteration. We define two families of languages: TLI = i or simply-typed list iteration of order i +3 with equality, and MLI = i or ML-typed list iteration of order i+3 with equality; we use i+3 since our list representation of databases requires at least order 3. We show that: FO-queries ` TLI = 0 ` MLI = 0 ` LOGSPACE-queries ` TLI = 1 = MLI = 1 = PTIME-queries ` TLI = 2 , where equality is no longer a primitive in TLI = 2 . We also show that ML type inference, restricted to fixed order, is polynomial in the size of the program typed. Since programming by using low order functionalities and type inference is common in functional languages, our results indicate that such programs suffice for expressing efficient computations and that their ML-types can be efficiently inferred.

. Currently much effort is being spent on providing objectoriented databases with ad hoc query facilities. In this paper we present a SQL-like query calculus whose major contribution lies in its inherent orthogonality and rigorous mathematical foundation. The calculus is essentially a calculus of complex values but it is defined independently of any concrete database model. The calculus can be used to formulate queries in value-based and object-based data models. Moreover it provides a general facility for the manipulation of complex values. 1 Introduction Object-oriented database systems (OODB) are usually embedded in a programming language environment providing full computational power. Consequently, designers of OODB at first did not feel the need to integrate ad hoc query facilities into their systems. However, it has been recognized that some associative retrieval is of importance even for OODB [8, 12, 13]. A well-tried ad hoc query language is SQL. SQL came up with relational da...

. In this paper a conceptually simple structural object model focusing on object types, attributes and ISA relationships is introduced. The model is derived mainly from an extended Entity-Relationship approach, but concepts from other semantic and object-oriented models have influenced its features. It is shown how high-level conceptual data models can be mapped to this model, and to what extent the object model subsumes classical modeling paradigms. 1 Introduction In recent years numerous data models for the conceptual modeling of information systems have been proposed. Among them there are semantic data models like SDM [13], IFO [3] and (extended) ER models [8, 9, 10, 24, 31, 34], complex object models like [1, 18, 26], purely object-based models like FDM [28] as well as object-based models with complex values such as [22]. All the approaches have different motivation, terminology, and aims. Here we aim to show you how some of these models can be translated into a conceptually simpl...

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 polynomial-time queries. Therefore, it was proposed to extend the nested algebra with a least-fixpoint construct, but the resulting language turned out to be too powerful: many inherently exponential queries could also be expressed. Two polynomial-time restrictions of the least-fixpoint closure of the nested algebra were proposed: the restricted least-fixpoint 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...