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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barendregt, H.: The Lambda Calculus: its Syntax and Semantics. North-Holland (1984)
Buneman, P., Davidson, S., Watters, A.: A semantics for complex objects and approximate answers. J. Comput. Syst. Sci. 43(1), 170–218 (1991)
Buneman, P., Frankel, R., Nikhil, R.: An implementation technique for database query languages. ACM Trans. Database Syst. 7(2), 164–186 (1982)
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)
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)
Kahrs, S.: Limits of ML-definability. In: Kuchen, H., Swierstra, S.D. (eds.) PLILP 1996. LNCS, vol. 1140, pp. 17–31. Springer, Heidelberg (1996)
Kahrs, S.: Well-going programs can be typed. In: Hofmann, M.O. (ed.) TLCA 2003. LNCS, vol. 2701, pp. 167–179. Springer, Heidelberg (2003)
Ohori, A., Buneman, P.: Polymorphism and type inference in database programming. ACM Trans. Database Syst. 21(1), 30–76 (1996)
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)
Schwichtenberg, H.: Definierbare funktionen in λ-kalkül mit typen. Archiv für Mathematische Logik und Grundlagenforschung 174, 113–114 (1976)
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)
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)
Wong, L.: Querying Nested Collections. PhD thesis, University of Pennsylvania (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Van den Bussche, J., Vansummeren, S. (2013). Well-Defined NRC Queries Can Be Typed. In: Tannen, V., Wong, L., Libkin, L., Fan, W., Tan, WC., Fourman, M. (eds) In Search of Elegance in the Theory and Practice of Computation. Lecture Notes in Computer Science, vol 8000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41660-6_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-41660-6_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41659-0
Online ISBN: 978-3-642-41660-6
eBook Packages: Computer ScienceComputer Science (R0)