An introduction to the completeness of languages for complex objects and nested relations

  • S. Abiteboul
  • C. Beeri
  • M. Gyssens
  • D. van Gucht
Part II Fundamental Issues
Part of the Lecture Notes in Computer Science book series (LNCS, volume 361)


Languages for models of nested relations and complex objects have been attracting considerable attention recently. Some of these languages are algebraic, others are calculus based, some are logic programming oriented. This paper describes these languages and surveys recent results about the expressive power of these languages. The emphasis is on completeness issues. The expressive power of the languages is described in terms of the three common types of completeness: calculus-completeness, BP-completeness and CH-completeness.


Logic Programming Transitive Closure Expressive Power Complex Object Atomic Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [ABe]
    Abiteboul, S., and C. Beeri, "On the power of languages for complex objects," Research report, INRIA and Hebrew University (April 1988).Google Scholar
  2. [ABi]
    Abiteboul, S., and Bidoit, N., "Non first normal form relations: an algebra allowing data restructuring", JCSS (1986)Google Scholar
  3. [AG]
    Abiteboul, S., and S. Grumbach, A logical approach to the manipulation of Complex Objects, Proc. EDBT (March 1988), Springer Verlag Lecture Notes in Computer Science 303.Google Scholar
  4. [AH1]
    Abiteboul S., and R. Hull, "IFO: A formal semantic database model," TODS (1988).Google Scholar
  5. [AH2]
    Abiteboul S., and R. Hull, "Object restructuring in semantic database models," Proc.ICDT, Roma (1986), to appear, TCS.Google Scholar
  6. [AU]
    Aho, A.V., J.D. Ullman, "Universality of data retrieval languages", Proc. POPL (1979).Google Scholar
  7. [ABW]
    Apt, K., H. Blair, and A. Walker, "Toward a Theory of Declarative Knowledge," In Foundations of deductive databases and logic programming, J. Minker (ed.), Morgan Kaufmann publishers (1988)Google Scholar
  8. [AV1]
    Abiteboul, S., V. Vianu, A Transaction Language Complete for Database Update and Specification, proc. ACM SIGACT-SIGMOD Symp. on Principles of Database Systems. (1987)Google Scholar
  9. [AV2]
    Abiteboul, S., V. Vianu, Procedural and Declarative Update Languages, proc. ACM SIGACT-SIGMOD Symp. on Principles of Database Systems. (1988)Google Scholar
  10. [Ba]
    Backus, J., "Can programming be liberated from the von Neuman style? A functional style of programming and its algebra of programs," 1977 Turing Award Lecture, CACM 21:8 (Aug. 1978).Google Scholar
  11. [Ban]
    Bancilhon, F., "On the completeness of query languages," Proc. 7th Symp. on Mathematical Foundations of Computer Science, Zakopane, Poland (1978).Google Scholar
  12. [BH]
    Bryce, D., and R. Hull, R., "SNAP: a graphics based schema manager," vProc. International Conf. on Data Engineering, Los Angeles (1986).Google Scholar
  13. [BK]
    Bancilhon, F., and S. Khoshafian, "A calculus for complex objects, Proc. 4th PODS (March 1985).Google Scholar
  14. [BNRST]
    Beeri, C.,S. Naqvi, R. Ramakrishnan, O. Shmueli, and S.Tsur, "Sets and Negation in a Logic Database Language," Proc. 6th PODS (March 1987)Google Scholar
  15. [BRS]
    Bancilhon, F., P. Richard, and M. Scholl, "Verso, a relational back end machine," Proc. Int'l Workshop on Database Machines, San Diego (1982).Google Scholar
  16. [C]
    Codd, E.F., "Relational completeness of database sublanguages," in Data Base Systems (R. Rustin, ed.) Prentice-hall, Englewood Cliffs, N.J. (1972).Google Scholar
  17. [Ch]
    Chen, L., "Extension of datalog with aggregation functions," IV journess bases de Donnees Avancees (March 1988).Google Scholar
  18. [Cha]
    Chamberlin, C. et al., "SEQUEL2: A unified approach to data definition, manipulation, and control," IBM Journal of Research and Development (1976).Google Scholar
  19. [CH]
    Chandra, A.K., and D.Harel, "Computable queries for relational database systems," JCSS 21:2 (1980).Google Scholar
  20. [DM]
    Dalhaus E., and J. Makowski, "Computable directory queries," manuscript, the Technion (August 1985).Google Scholar
  21. [DiP]
    Di paola, R.A., "The recursive unsolvability of the decision problem for the class of definite formulas," JACM (April 1969).Google Scholar
  22. [Fa]
    Fagin, R., "Horn clauses and database dependencies," JACM 29:4 (Oct. 1982).Google Scholar
  23. [FT]
    Fischer, P., and S. Thomas, "Operators for non-first-normal-form relations," Proc. 7th COMPSAC, Chicago,(Nov. 1983).Google Scholar
  24. [G]
    Gyssens, M., "The extended nested relational algebra", Techn. Rep. 87-11, University of Antwerp, 1987.Google Scholar
  25. [GVG1]
    Gyssens, M., and D. Van Gucht, "The Powerest Operator as an Algebraic Tool for Understanding Least Fixpoint Semantics in the Context of Nested Relations", Techn. Rep. 233, Indiana University, Bloomington, 1987.Google Scholar
  26. [GVG2]
    Gyssens, M., and D. Van Gucht, "The Powerset Algebra as a Result of Adding Programming Constructs to the Nested Relational Algebra", Proc. ACM-SIGMOD Conference on Management of Data, Chicago (1988).Google Scholar
  27. [H]
    Hull, R., "A Survey of Theoretical Research on Typed Complex Database Objects," manuscript, USC (1986).Google Scholar
  28. [Ha]
    Hardgrave, W.T., "Ambiguity in processing Boolean queries on TDMS tree structures: A study of four different philosophies," T.R. University of Maryland (1978).Google Scholar
  29. [HS]
    Hull, R. and J. Su, "On the expressive power of database queries with intermediate types," Proc. 7th PODS (March 1988).Google Scholar
  30. [HY]
    Hull, R., and C. Yap, "The format model: A theory of database organization," JACM 31:3 (July 1984).Google Scholar
  31. [J]
    Jacobs, B., "On database logic," JACM 29:2 (April 1982).Google Scholar
  32. [JW]
    Jacobs, B., and C. Walczak, "A generalized Query-by-Example data manipulation language based on database logic," IEEE Trans. on Software Engineering (1883).Google Scholar
  33. [JS]
    Jaeschke, B., and H.-J. Schek, "Remarks on the algebra of non first normal form relations," Proc. 1st PODS (March 1982).Google Scholar
  34. [Kl]
    Klug, A., "Equivalence of relational algebra and calculus query languages having aggregate functions," JACM 29:3 (July 1982).Google Scholar
  35. [Ku]
    Kuper, G.M., "Logic Programming with Sets," Proc.6th PODS (1987)Google Scholar
  36. [KV1]
    Kuper, G.M., M.Y. Vardi, "A new approach to database logic," Proc. 3rd PODS (1984)Google Scholar
  37. [KV2]
    Kuper, G.M., M.Y. Vardi, "On the expressive power of the logical data model," Proc. ACM SIGMOD Int'l Conf. on Management of Data (1985).Google Scholar
  38. [L1]
    Lloyd, J., Foundations of logic programming, Springer Verlag (1984).Google Scholar
  39. [Mak]
    Makinouchi, A., "A consideration on normal form of not-necessarily normalized relations in the relational model," Proc. 3rd VLDB (Oct. 1977).Google Scholar
  40. [N]
    Naqvi, S.A., "A Logic for Negation in Database Systems," Proc. Foundations of Deductive Databases and Logic Programming (1986)Google Scholar
  41. [OOM]
    Ozsoyoglu, G, Z.M. Ozsoyoglu, and V. Matos, "Extending relational algebra and relational calculus with set-valued attrributes and aggregate functions," TODS 12:4 (Dec. 1987).Google Scholar
  42. [Par]
    Paredaens, J., "On the expressive power of relational algebra," Inf. Processing letters (1978)Google Scholar
  43. [PS]
    Parent, C., and S. Sppacapietra, "Un modele et une algebre pour les bases de donnees de type entite-relation," in technique et Science Informatique (1985)Google Scholar
  44. [Pau]
    Pauthe, P. "EVER, un editeur de V-relations," These de Doctorat, Universite d'Orsay (1985).Google Scholar
  45. [PA]
    Pistor, P., and F. Andersen, "Principles for designing a generalized NFNF data model with an SQL-type language interface," T.R. IBM Heidelberg (1986).Google Scholar
  46. [RKB]
    Roth, M.A., Korth, H.F., and D. Batory, "SQL/NF — A query langauge for — 1NF relational databases,’ T.R., University of Texas, Austin (1986).Google Scholar
  47. [RKS]
    Roth, M.A., H.F. Korth, and A. Silberschatz, "Extended algebra and calculus for — NF relational databases," manuscript, TR-84-36, Department of Computer Science, University of Texas at Austin, 1984, revised, 1985, to appear, TODS.Google Scholar
  48. [RS]
    Ramakrishnan, R., and A. Silberschatz, "The molecular relation data model", T.R. University of Texas, Austin (1986).Google Scholar
  49. [Sh]
    Shipman, D. "The functional data model and the data language DAPLEX, TODS 6:1 (1981).Google Scholar
  50. [SP]
    Schek, H.-J., and P. Pistor, "Data structures for integrated database management and information retrieval system," Proc. Int'l Conf. on Very Large Data Bases, Mexico (1982).Google Scholar
  51. [SS]
    Schek H.-J, and M. Scholl, "An algebra for the relational model with relation-valued attributes," Information Systems. 11:2 (1986).Google Scholar
  52. [St-]
    Stonebraker, M., and L. Rowe, "The design of POSTGRESS," Proc. ACM SIGMOD Int'l Conf. on Management of Data (1986).Google Scholar
  53. [U1]
    Ullman,J.D., Principles of database systems, Computer Science Press, 2nd ed. (1982).Google Scholar
  54. [Va]
    Vardi, M. Y., "The decision problem for database dependencies," Inf. Proc. Letters (Oct. 1981).Google Scholar
  55. [VGT]
    Van Gelder, A., and R. Topor, "Safety and correct translation of relational calculus queries," Proc. 6th PODS (1987).Google Scholar
  56. [VGe]
    Van Gelder, A., "Negation as Failure Using Tight Derivations for General Logic Programs," In Foundations of deductive databases and logic programming, J. Minker (ed.), Morgan Kaufmann publishers (1988)Google Scholar
  57. [VGu]
    Van Gucht, D., "On the expressive power of the extended relational algebra for the nonnormalized relational model, Proc. 6th PODS (1987).Google Scholar
  58. [Ver]
    Verso, J., "VERSO: A database machine based on non 1NF relations," rapport de Recherche INRIA 523 (1986).Google Scholar
  59. [Za]
    Zaniolo, C., "The database language GEM," Proc. of ACM SIGMOD Int'l Conf. on Management of Data (1983).Google Scholar
  60. [Zl]
    Zloof, M., "Query by example: a database language," IBM Systems Journal (1977).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • S. Abiteboul
    • 1
  • C. Beeri
    • 2
  • M. Gyssens
    • 3
  • D. van Gucht
    • 4
  1. 1.INRIAFrance
  2. 2.The Hebrew UniversityIsrael
  3. 3.University of AntwerpBelgium
  4. 4.Indiana UniversityUSA

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