Abstract
This paper proposes an algebraic semantics approach for data and object modeling. The approach captures the main concepts of object systems, namely : class, method, object identity, inheritance, overriding, overloading, late and early binding, collection types and persistence objects. The proposed model follows the algebraic aspects of relational database tradition; that is, the clear separation between schema, types (or domains), instance and query. For this reason it is enable to support an algebraic query language in the style of the relational algebra. Our approach also provides a rigorous mathematical treatment of null values in the object-oriented systems.
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References
M. Abadi and L. Cardelli. A Theory of Objects. Springer-Verlag, 1996.
S. Abiteboul and C. Berri. On the Power of languages for Manipulation of Complex Objects. In Proceedings of International Workshop on Theory and Applications of Nested Relations and Complex Objects, 1988.
S. Abiteboul and R. Hull and V. Vianu. Foundation of Databases, Addison-Wesley, 1995.
F. Bancilhon and S. Cluet and C. Delobel. A query language for O2. In François Bancilhon, Claude Delobel, and Paris Kanellakis, editors, Building an Object-Oriented Database System, The Story of O2. Morgan Kaufmann, 1992.
V. Breazu-Tannen and P. Buneman and S. Naqvi. Structural Recursion as a Query Language. In Proceedings of the Third International Workshop on Database Programming Language: Bulk types and Persistent Data, pages 9–19, 1991.
V. Breazu-Tannen and R. Subrahmaniam. Logical and Coputational Aspects of Programming with Sets/Bags/Lists. In 18th International Colloquiumon Automata, Languages and Programming, Madrid, Spain, Springer Verlag, LNCS 510, pages 60–75,1991.
P. Buneman and S. Naqvi and V. Tannen and Limsoon Wong. Principle of Programming with Complex Objects and Collection types. Theorical computer Science, 149:3–48, 1995.
G. Castagna. Object-Oriented Programming. A Unified Foundation, Birkhäuser, 1997.
R. Cattel. The Object Databases Standard: ODMG-93, Release 1.2. Morgan Kaufmann, 1996.
S. Cluet. Designing OQL: Allowing object to be queried. Information Systems 23(5), pages 279–305, 1998.
S. Cluet and G. Moerkeotte. Nested Queries in Object Bases. In Fifth International Workshop on database Programming Languages, pages 226–242, 1993.
L. Fegaras. Query Unnesting in Object-Oriented Databases. Proceedings of the ACM SIGMOD International Conference on Managmenent of data, Seattle, Washington, pages 49–60, 1998.
L. Fegaras and D. Maier. Towards an Effective Calculus for Object query languages. In Proc. of ACM SIGMOD International Conference on Management of Data, pages 47–58,1995.
J. Frohn and G. Lausen and H. Uphogg. Access to Objects by Path Expressions and Rules. Proceedings of the 20th VLDB Conference, Santiago, pages 273–284, 1994.
R. Herzig and M. Gogolla. A SQL-like Query Calculus for Object-Oriented Database Systems. International Symposium Object-Oriented Methodologies and Systems, LNCS 858, pages 20–39, 1994.
M. Kifer and W. Kim and Y. Sagiv. Querying Object-oriented databases. In Proc. of the ACM SIGMOD Conference on Management of Data, pages 393–402, 1992.
W. Kim. Modern Database Systems. The Object Model, Interoperability, and Beyond, Addison-Wesley, 1995.
W. Kim. A Model of queries for Object-orienrted databases. In Proc. of the Intl. Conference on VLDB, pages 423–432, 1989.
G. Lausen and G. Vossen. Models and Languages of Object-Oriented Databases, Addison-Wesley, 1997.
C. Lecluse and P. Richard and V. Velez. The O2 Data Model, In François Bancilhon, Claude Delobel, and Paris Kanellakis, editors, Building an Object-Oriented Database System, The Story of O2 Morgan Kaufmann, 1992.
S.K. Lellahi. Type de collection et Monades. Acte des Journées Catégories, Algèbres, Esquisses et Neo-esquisses, CAEN, pages 109–114, 1994.
S.K. Lellahi and N. Spyratos. Towards a Categorical data model Supporting Structural objects and Inheritance. East/West Database Workshop, LNCS 504, 1991, pp 86–105.
S.K. Lellahi and R. Souah and N. Spyratos. An algebraic query language for Object-Oriented data Models. DEXA97, LNCS N0 1308, pages 519–528, 1997.
S.K. Lellahi and N. Spyratos and M'B. Thiam. Functional Dependencies and the Semantics of Class extensions. Journal of Computing and Information, Special issue: Proceedings of 8th ICCT 2(1), pages 892–913, 1996.
S.K. Lellahi and V. Tannen. A calculus for collections and aggregates. Category and Computer Science, LNCS 1290, pages 261–280, 1997.
M. Levene and G. Loizou. A Guided Tour of relational Databases and Beyond, Springer, 1999.
P. Niemeyer and J. Peck. Exploring Java. O'Reilly & Associates Inc, 1996.
M.A. Roth and H.F. Korth and A. Silberschatz. The theory of Non-First-Normalform Relational databases. TR-84-36, University of Texas at Austin, 1986.
H.J. Schek and M.H. Sholl. The Relational Model with Relational valued Attributes. Information Systems, 11(2):137–147.
R. Souah. Une Sémantique Algébrique pour Bases de données Orientées objet. PhD thesis, Université Paris-sud (Orsay), 1999.
M'B. Thiam. Dépendances Fonctionnelles et Consistance pour Base de données objet, PhD thesis, Université Paris 1 Panthéon-Sorbonne, 1998.
Y. Vassiliou. Null Values in Database Management: a Denotational Semantics Approach. Proceedings of ACM SIGMOD International Conference on Management of Data, pages 162–169, 1979.
C. Zaniolo. Database Relations with Null Values. Journal of Computer and System Sciences, 28:142–166, 1984.
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Lellahi, K. (2002). Modeling Data and Objects: An Algebraic View Point. In: Khosrovshahi, G.B., Shokoufandeh, A., Shokrollahi, A. (eds) Theoretical Aspects of Computer Science. TACSci 2000. Lecture Notes in Computer Science, vol 2292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45878-6_4
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DOI: https://doi.org/10.1007/3-540-45878-6_4
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