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Fundamental Concepts of Object Oriented Databases
 ACTA CYBERNETICA
, 1993
"... It is claimed that object oriented databases (OODBs) overcome many of the limitations of the relational model. However, the formal foundation of OODB concepts is still an open problem. Even worse, for relational databases a commonly accepted datamodel existed very early on whereas for OODBs the uni ..."
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Cited by 33 (19 self)
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It is claimed that object oriented databases (OODBs) overcome many of the limitations of the relational model. However, the formal foundation of OODB concepts is still an open problem. Even worse, for relational databases a commonly accepted datamodel existed very early on whereas for OODBs the unification of concepts is missing. The work reported in this paper contains the results of our first investigations on a formally founded object oriented datamodel (OODM) and is intended to contribute to the development of a uniform mathematical theory of OODBs. A clear distinction between objects and values turns out to be essential in the OODM. Types and Classes are used to structure values and objects repectively. Then the problem of unique object identification occurs. We show that this problem can be be solved for classes with extents that are completely representable by values. Such classes are called valuerepresentable. Another advantage of the relational approach is the existence o...
Equal Rights for Functional Objects or, The More Things Change, The More They Are the Same
, 1993
"... DATA TYPES A. Comparing Type Objects There has been as much confusion over type identity as there has been over object identity, although the type identity problem is usually referred to as the type equivalence problem [Aho86,s.6.3] [Wegbreit74] [Welsh77]. The type identity problem is to determine ..."
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Cited by 22 (7 self)
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DATA TYPES A. Comparing Type Objects There has been as much confusion over type identity as there has been over object identity, although the type identity problem is usually referred to as the type equivalence problem [Aho86,s.6.3] [Wegbreit74] [Welsh77]. The type identity problem is to determine when two types are equal, so that type checking can be done in a programming language. 22 Algol68 takes the point of view of "structural" equivalence, in which nonrecursive types that are built up from primitive types using the same type constructors in the same order should compare equal, while Ada takes the point of view of "name" equivalence, in which types are equivalent if and only if they have the same name. We will ignore the software engineering issues of which kind of type equivalence makes for betterengineered programs, and focus on the basic issue of type equivalence itself. We note that if a type system offers the type TYPEi.e., it offers firstclass representations of typ...
How to Comprehend Queries Functionally
, 1999
"... Compilers and optimizers for declarative query languages use some form of intermediate language to represent userlevel queries. The advent of compositional query languages for orthogonal type systems (e.g. OQL) calls for internal query representations beyond extensions of relational algebra. This w ..."
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Cited by 11 (3 self)
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Compilers and optimizers for declarative query languages use some form of intermediate language to represent userlevel queries. The advent of compositional query languages for orthogonal type systems (e.g. OQL) calls for internal query representations beyond extensions of relational algebra. This work adopts a view of query processing which is greatly influenced by ideas from the functional programming domain. A uniform formal framework is presented which covers all query translation phases, including userlevel query language compilation, query optimization, and execution plan generation. We pursue the typebased design  based on initial algebras  of a core functional language which is then developed into an intermediate representation that ts the needs of advanced query processing. Based on the principle of structural recursion we extend the language by monad comprehensions (which provide us with a calculusstyle sublanguage that proves to be useful during the optimization of nested...
Optimizing Queries with Object Updates
 journal of Intelligent Information Systems
, 1998
"... Objectoriented databases (OODBs) provide powerful data abstractions and modeling facilities but they usually lack a suitable framework for query processing and optimization. Even though there is an increasing number of recent proposals on OODB query optimization, only few of them are actually focus ..."
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Cited by 10 (1 self)
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Objectoriented databases (OODBs) provide powerful data abstractions and modeling facilities but they usually lack a suitable framework for query processing and optimization. Even though there is an increasing number of recent proposals on OODB query optimization, only few of them are actually focused on query optimization in the presence of object identity and destructive updates, features often supported by most realistic OODB languages. This paper presents a formal framework for optimizing objectoriented queries in the presence of side effects. These queries may contain object updates at any place and in any form. We present a language extension to the monoid comprehension calculus to express these objectoriented features and we give a formal meaning to these extensions. Our method is based on denotational semantics, which is often used to give a formal meaning to imperative programming languages. The semantics of our language extensions is expressed in terms of our monoid calculu...
A Uniform Calculus for Collection Types
 OREGON GRADUATE INSTITUTE OF SCIENE & TECHNOLOGY
, 1994
"... We present a new algebra for collection types based on monoids and monoid homomorphisms. The types supported in this algebra can be any nested composition of collection types, including lists, sets, multisets (bags), vectors, and matrices. We also define a new calculus for this algebra, called mo ..."
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Cited by 9 (0 self)
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We present a new algebra for collection types based on monoids and monoid homomorphisms. The types supported in this algebra can be any nested composition of collection types, including lists, sets, multisets (bags), vectors, and matrices. We also define a new calculus for this algebra, called monoid comprehensions, that captures operations involving multiple collection types in declarative form. This algebra can easily capture the semantics of many objectoriented database query languages that support mixed collection types, such as the OQL language of the ODMG93 standard. In addition, it is ideal for expressing data parallelism and nested parallelism and can be effectively translated onto many parallel architectures. We present a normalization algorithm that reduces any expression in our algebra to a canonical form which, when evaluated, generates very few intermediate data structures. These canonical forms are amenable to a higher degree of parallelism than the original...
Extensible Safe ObjectOriented Design of Database Applications
 University of Rostock
, 2000
"... The formal foundation of objectoriented databases is still an open problem. In this paper a formalization of kernel objectoriented design concepts is achieved by an automatizable transformation into a specification language with a clear mathematical semantics. This approach allows objectoriented ..."
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Cited by 8 (8 self)
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The formal foundation of objectoriented databases is still an open problem. In this paper a formalization of kernel objectoriented design concepts is achieved by an automatizable transformation into a specification language with a clear mathematical semantics. This approach allows objectoriented design to be extensible. The preservation of advantages of relational databases requires the de nability of generic operations for the insertion, deletion and update of single objects. It is shown that such generic operations can only be defined for valuerepresentable classes. The possibility to detect valuerepresentability contributes to the safety for objectoriented design.
Foundations of Object Oriented Database Concepts
 Bericht FBIHHB157/92, Fachbereich Informatik, Universität
, 1992
"... It is claimed that object oriented databases (OODBs) overcome many of the limitations of the relational model. However, the formal foundation of OODB concepts is still an open problem. Even worse, for relational databases a commonly accepted datamodel existed very early on whereas for OODBs the unif ..."
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Cited by 5 (4 self)
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It is claimed that object oriented databases (OODBs) overcome many of the limitations of the relational model. However, the formal foundation of OODB concepts is still an open problem. Even worse, for relational databases a commonly accepted datamodel existed very early on whereas for OODBs the unification of concepts is outstanding. Our research in Hamburg and Rostock is directed towards a formally founded object oriented datamodel (OODM) and to contribute to the development of a uniform mathematical theory of OODBs. This report contains the results of our first investigations on the OODM. A clear distinction between objects and values turns out to be essential in the OODM. Types and Classes are used to structure values and objects repectively. Then the problem of unique object identification occurs. We show that this problem can be be solved for classes with extents that are completely representable by values. Such classes are called valuerepresentable. The finiteness of a database and the existence of finitely representable rational tree types are sufficient to decide valuerepresentability. Another advantage of the relational approach is the existence of structurally determined
Fundamentals of Object Oriented Database Modelling
, 1996
"... Solid theoretical foundations of object oriented databases (OODBs) are still missing. The work reported in this paper contains results on a formally founded object oriented datamodel (OODM) and is intended to contribute to the development of a uniform mathematical theory of OODBs. A clear distinctio ..."
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Cited by 2 (2 self)
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Solid theoretical foundations of object oriented databases (OODBs) are still missing. The work reported in this paper contains results on a formally founded object oriented datamodel (OODM) and is intended to contribute to the development of a uniform mathematical theory of OODBs. A clear distinction between objects and values turns out to be essential in the OODM. Types and classes are used to structure values and objects repectively. This can be founded on top of any underlying type system. We outline different approaches to type systems and their semantics and claim that OODB theory on top of arbitrary type systems leads to type theory with topostheoretically defined semantics. On this basis the known solutions to the problems of unique object identification and genericity can be generalized. It turns out that extents of classes must be completely representable by values. Such classes are called valuerepresentable. As a consequence object identifiers degenerate to a pure...
The Type Concept in OODB Modelling and its Logical Implications
, 2000
"... Conceptual modelling requires a solid mathematical theory of concepts concerning the collection of concepts used in a specific, but broad enough field. The field considered in this paper is database modelling. Here object orientation in the widest sense has been identified as a unifying conceptual u ..."
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Cited by 2 (2 self)
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Conceptual modelling requires a solid mathematical theory of concepts concerning the collection of concepts used in a specific, but broad enough field. The field considered in this paper is database modelling. Here object orientation in the widest sense has been identified as a unifying conceptual umbrella that encompasses all relevant datamodels. The theory of object oriented databases has brought to light the fundamental distinction between the concepts of objects and values and correspondingly types and classes. This can be founded on top of any underlying type system. Thus, expressiveness of a datamodel basically depends on the type concept, from which the other concepts can be derived. In order to achieve a uniform mathematical theory we outline different type systems and their semantics and claim that OODB theory on top of arbitrary type systems leads to type theory with topostheoretically defined semantics. On this basis the known solutions to the problems of unique ...