Well-Defined NRC Queries Can Be Typed

(Extended Abstract)
  • Jan Van den Bussche
  • Stijn Vansummeren

Abstract

We study the expressive power of the static type system of the Nested Relational Calculus \(\mathcal{NRC}\) and show that on so-called homogeneous input and output types, the \(\mathcal{NRC}\) type system is expressively complete: every untyped but homogeneously well-defined \(\mathcal{NRC}\) expression can be equivalently expressed by a well-typed expression. The \(\mathcal{NRC}\) static type system hence does not limit the expressive power of the query writer.

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References

  1. 1.
    Barendregt, H.: The Lambda Calculus: its Syntax and Semantics. North-Holland (1984)Google Scholar
  2. 2.
    Buneman, P., Davidson, S., Watters, A.: A semantics for complex objects and approximate answers. J. Comput. Syst. Sci. 43(1), 170–218 (1991)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Buneman, P., Frankel, R., Nikhil, R.: An implementation technique for database query languages. ACM Trans. Database Syst. 7(2), 164–186 (1982)CrossRefGoogle Scholar
  4. 4.
    Buneman, P., Naqvi, S.A., Tannen, V., Wong, L.: Principles of programming with complex objects and collection types. Theor. Comput. Sci. 149(1), 3–48 (1995)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Buneman, P., Pierce, B.: Union types for semistructured data. In: Connor, R., Mendelzon, A. (eds.) DBPL 1999. LNCS, vol. 1949, pp. 184–207. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Kahrs, S.: Limits of ML-definability. In: Kuchen, H., Swierstra, S.D. (eds.) PLILP 1996. LNCS, vol. 1140, pp. 17–31. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  7. 7.
    Kahrs, S.: Well-going programs can be typed. In: Hofmann, M.O. (ed.) TLCA 2003. LNCS, vol. 2701, pp. 167–179. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Ohori, A., Buneman, P.: Polymorphism and type inference in database programming. ACM Trans. Database Syst. 21(1), 30–76 (1996)CrossRefGoogle Scholar
  9. 9.
    Ohori, A., Buneman, P., Breazu-Tannen, V.: Database programming in Machiavelli—a polymorphic language with static type inference. In: Clifford, J., Lindsay, B., Maier, D. (eds.) Proceedings of the 1989 ACM SIGMOD International Conference on the Management of Data. SIGMOD Record, vol. 18(2), pp. 46–57. ACM Press (1989)Google Scholar
  10. 10.
    Schwichtenberg, H.: Definierbare funktionen in λ-kalkül mit typen. Archiv für Mathematische Logik und Grundlagenforschung 174, 113–114 (1976)Google Scholar
  11. 11.
    Van den Bussche, J., Van Gucht, D., Vansummeren, S.: A crash course on database queries. In: Proceedings of the Twenty-Sixth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS), pp. 143–154. ACM (2007)Google Scholar
  12. 12.
    Van den Bussche, J., Van Gucht, D., Vansummeren, S.: Well-definedness and semantic type-checking for the nested relational calculus. Theor. Comput. Sci. 371(3), 183–199 (2007)CrossRefMATHGoogle Scholar
  13. 13.
    Wong, L.: Querying Nested Collections. PhD thesis, University of Pennsylvania (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jan Van den Bussche
    • 1
    • 2
  • Stijn Vansummeren
    • 3
  1. 1.Hasselt UniversityBelgium
  2. 2.Transnational University of LimburgBelgium
  3. 3.Université Libre de BruxellesBelgium

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