Abstract
Data collections form the basis for the representation and manipulation of data in database systems. We describe an algebra for manipulating data collections. It has been developed using constructive logic, and is a generalisation of relational algebra. We have applied the proofs-as-programs paradigm of intiutionistic type theory for deriving executable functions from specifications of algebra operations. The properties of algebra operators such as associativity, commutativity and distributivity have been verified using the same formal system.
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References
Beeri, C., and Kornatzky, Y. Algebraic Optimization of Object-Oriented Query Languages. In Abiteboul, S., and Kanellakis, P.C.(Eds.), ICDT'90, LNCS, Springer-Verlag, 1990, pp. 72–88.
Breazu-Tannen, V., and Subrahmanyam,R. Logical and Computational Aspects of Programming with Sets/Bags/Lists. In LNCS 510: Proc. of 18th International Colloquium on Automata, Languages, and Programming, Springer Verlag, 1991, pp 60–75.
Buneman, P., Libkin, L., Suciu, D., Tannen, V., and Wong, L. Comprehension Syntax. SIGMOD Record, Vol.23, No.1, March 1994, pp 87–96.
Constable,R.L., et al. Implementing Mathematics with the Nuprl Proof Development System, Prentice-Hall, 1986.
Constable, R.L. Type Theory as a Foundation for Computer Science. In Ito, T., and Meyer, A.R. (Eds.), Theoretical Aspects of Computer Software, Proc. Intl. Conf., Sendai, Japan, Sept 1991, Springer-Verlag, pp 226–243.
Kanellakis, P., and Schmidt, J.W. (Eds.). Database Programming Languages: Bulk Types & Persistent Data, The Third International Workshop Proc, Aug 1991, Nafplion, Greece.
Martin-Lof, P. Constructive Mathematics and Computer Programming. In Sixth International Congress for Logic, Methodology, and Philosophy of Science, pp. 153–175, North-Holland, 1982.
Martin-Lof, P. Intuitionistic Type Theory. In Studies in Proof Theory Lecture Notes, Bibliopolis, Napoli, 1984.
Mendler, P. Inductive Definition in Type Theory. PhD thesis, Cornell University, Ithaca, NY, 1988.
The Nuprl Group. The Nuprl Proof Development System, Version 3.2 Reference Manual and User's Guide. Dept of Computer Science, Cornell University, September 1991.
Rajagopalan, P. A Type Theory Approach to the Specification and Synthesis of Database models. Ph.D. thesis, University of Western Australia, December 1993.
Rajagopalan, P., and Tsang, C.P. A Type Theory Approach to the Development of Database Concepts. In Proc. International Symp. on Advanced Database Technologies and Their Integration (ADTI'94), Nara, Japan, October 1994.
Ullman, J.D. Principles of Database and Knowledge-base Systems. Computer Science Press, 1988.
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Rajagopalan, P., Tsang, C.P. (1995). A generic algebra for data collections based on constructive logic. In: Alagar, V.S., Nivat, M. (eds) Algebraic Methodology and Software Technology. AMAST 1995. Lecture Notes in Computer Science, vol 936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60043-4_77
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DOI: https://doi.org/10.1007/3-540-60043-4_77
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