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Prototyping a Categorical Database in P/FDM

  • Conference paper
Advances in Databases and Information Systems

Part of the book series: Workshops in Computing ((WORKSHOPS COMP.))

Abstract

The relational data model uses set theory to provide a formal background, thus ensuring a rigorous mathematical data model with support for manipulation. The newer generation database models are based on the object-oriented programming paradigm, and so fall short of having a formal background, especially in some of the more complex data manipulation areas. We use category theory to provide a formalism for object databases, known as the product model. This paper will describe our formal model for the key aspects of object databases. In particular, we will examine how this model deals with three of the most important problems inherent in object databases, those of queries, closure and views. As well as this, we investigate the more common database concepts, such as keys, relationships, aggregation, etc. We will implement a prototype of this model using P/FDM, a semantic data model database system based on the functional model of Shipman, with object-oriented extensions.

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References

  1. ISO-ANSI SQL 3 Working Draft. Digital Equipment Corporation, Massachusetts, March 1994.

    Google Scholar 

  2. M. Atkinson, et. al. The Object-Oriented Database System Manifesto. In F. Bancilhon, et. al. The Story of O 2 : Implementing an Object-Oriented Database System, Morgan Kaufmann, 1992.

    Google Scholar 

  3. M. Barr, C. Wells. Category Theory for Computing Science. Prentice-Hall International Series in Computer Science, 1990.

    MATH  Google Scholar 

  4. B. Cadish, Z. Diskin. Algebraic Graph-Oriented = Category Theory Based: Categorical Data Modelling Manifesto. Frame Inform Systems, Database Design Laboratory, Latvija, DBDL Research Report FIS/DBDL-94–02, July 1994.

    Google Scholar 

  5. L. Cardelli. A Semantics of Multiple Inheritance. LNCS, 173:51–67, 1984.

    MathSciNet  Google Scholar 

  6. P. P. Chen. The Entity-Relationship Model: Toward a Unified View of Data. ACM TODS, 1(1):9–36, March 1976.

    Article  Google Scholar 

  7. J. Demetrovics, L. Libkin, and I. B. Muchnik. Functional Dependencies in Relational Databases: A Lattice Point of View. Discrete Applied Mathematics, 40(2):155–185, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  8. E. Dennis-Jones, D. E. Rydeheard. Categorical ML — Category-Theoretic Modular Programming. Formal Aspects of Computing, 5(4):337–366, 1993.

    Article  MATH  Google Scholar 

  9. L. Duponcheel. Gofer Experimental Prelude. Alcatel, Belgium, 1994.

    Google Scholar 

  10. S. M. Embury, et. al. User Manual for P/FDM Version 9.0. University of Aberdeen, Technical Report AUCS/TR9501, January 1995.

    Google Scholar 

  11. P. J. Freyd, A. Scedrov. Categories, Allegories. North-Holland Mathematical Library 39, 1990.

    MATH  Google Scholar 

  12. P. M. D. Gray, K. G. Kulkarni, and N. W. Paton. Object-Oriented Databases: A Semantic Data Model Approach. Prentice-Hall International Series in Computer Science, 1992.

    MATH  Google Scholar 

  13. K. M. Kuper, M. Y. Vardi. The Logical Data Model. ACM TODS, 18(3):379–413, 1993.

    Article  MathSciNet  Google Scholar 

  14. S. Mac Lane, I. Moerdijk. Sheaves in Geometry and Logic, A First Introduction to Topos Theory. Springer-Verlag 1991.

    Google Scholar 

  15. D. A. Nelson, B. N. Rossiter, and M. A. Heather. The Functorial Data Model — An Extension to Functional Databases. University of Newcastle upon Tyne, Technical Report Series, No. 488, 1994.

    Google Scholar 

  16. D. A. Nelson, B. N. Rossiter. Suitability of Programming Languages for Categorical Databases. University of Newcastle upon Tyne, Technical Report Series, No. 511, March 1995.

    Google Scholar 

  17. S. L. Osborn. Testing for Existence of a Covering Boyce Codd Normal Form. Information Processing Letters, 8(1): 11–14, January 1979.

    Article  MathSciNet  MATH  Google Scholar 

  18. B. N. Rossiter, M. A. Heather. Applying Category Theory to Databases. Presented to 8th British Colloquium for Theoretical Computing Science in March 1992, published as Technical Report No. 407, University of Newcastle upon Tyne.

    Google Scholar 

  19. B. N. Rossiter, M. A. Heather. Database Architecture and Functional Dependencies Expressed with Formal Categories and Functors. University of Newcastle upon Tyne, Technical Report Series, No. 432, 1993. Categorical

    Google Scholar 

  20. D. E. Rydeheard, R. M. Burstall. Computational Category Theory. Prentice-Hall International Series in Computer Science, 1988.

    MATH  Google Scholar 

  21. D. W. Shipman. The Functional Data Model and the Data Language DAPLEX. ACM TODS, 6(1):140–173, March 1981.

    Article  Google Scholar 

  22. SICStus Prolog User’s Manual, Edition 2.1, Patch #7. Swedish Institute of Computer Science, January 1993.

    Google Scholar 

  23. H. Simmonds. Lecture Notes for SERC School on Logic for Information Technology. University of Leeds, 1990.

    Google Scholar 

  24. J. Smith, D. Smith. Data Abstraction, Aggregation and Generalization. ACM TODS, 2(2):105–133, 1977.

    Article  Google Scholar 

  25. M. Stonebraker, L. A. Rowe. The Design of Postgres. In Proceedings ACM SIGMOD Conference, pages 340–355, 1986.

    Google Scholar 

  26. M. Stonebraker. Object-Relational Database Systems. Montage Software Inc., 1994.

    Google Scholar 

  27. D. Tsichritzis. ANSI/X3/SPARC DBMS Framework, Report of the Study Group on Data Base Management Systems. Information Systems, 3(3):173–192, 1978.

    Article  Google Scholar 

  28. J. D. Ullman. Principles of Database and Knowledge-Base Systems 1. Computer Science Press, 1988.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computing Science, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, UK

    D. A. Nelson & B. N. Rossiter

Authors
  1. D. A. Nelson
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  2. B. N. Rossiter
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Klagenfurt, Universitätsstraße 65, A-9020, Klagenfurt, Austria

    Johann Eder

  2. Institute for Problems of Informatics, Russian Academy of Sciences, Vavilov Street 30/6, 117900, V-334, Moscow, Russian Federation

    Leonid A. Kalinichenko

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© 1996 British Computer Society

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Nelson, D.A., Rossiter, B.N. (1996). Prototyping a Categorical Database in P/FDM. In: Eder, J., Kalinichenko, L.A. (eds) Advances in Databases and Information Systems. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-1486-4_27

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  • DOI: https://doi.org/10.1007/978-1-4471-1486-4_27

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-76014-6

  • Online ISBN: 978-1-4471-1486-4

  • eBook Packages: Springer Book Archive

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