The logic of a relational data manipulation language

ABSTRACT

A logic for a relational data manipulation language is defined by augmenting a known logic of programs with rules for two new statements: the relational assignment, which assign a relational expression to a relation, and the random tuple selection, which extracts an arbitrary tuple from a relation. The usual operations on relations-retrieve, insert, delete, update-are then defined as special cases of the relational assignment, and the for-each construct scanning a relation tuple by tuple is introduced with the help of the random tuple selection.

REFERENCES

• 1: {BE1} Bernstein, P. A. et al. "The Concurrency Control Mechanism of SDD-1: A System for Distributed Databases", Computer Corporation of America Tech. Rep. 77-09, Dec. 1977.
• 2: {BE2} Bernstein, P. A. et al. "An Approach to the Design and Implementation of Interactive Information Systems", (Draft, Nov. 1977).
• 3: {CA1} Cadiou, J. M. "On Semantic Issues in the Relational Model of Data", Proc. Int. Symp. on Math. Foundations of Computer Science, Gdansk, Poland, "Lecture Notes in Computer Science", Springer-Verlag, Sept. 1976.
• 4: {CA2} Casanova, M. A. "The Logic of a Data Manipulation Language" (technical report in progress).
• 5: {CH1} Chamberlin, D. D. et al. "SEQUEL 2: A Unified Approach to Data Definition, Manipulation and Control", IBM Tech. Rep. RJ1798, June 1976.
• 6: {CO1} Codd, E. F. "A Database Sublanguage Founded on the Relational Calculus", Proc. 1971 ACM SIGFIDET Workshop on Data Description, Access and Control.
• 7: E. F. Codd, A relational model of data for large shared data banks, Communications of the ACM, v.13 n.6, p.377-387, June 1970 [doi>10.1145/362384.362685]
• 8: {CO3} Cook, S. A. "Axiomatic and Interpretative Semantics for an ALGOL Fragment", TR-79, Univ. of Toronto, Feb. 1975.
• 9: {ES1} Eswaran, K. P. and D. D. Chamberlin. "Functional Specifications of a Subsystem for Database Integrity", Proc. of the Int. Conf. on Very Large Data Bases, 1975.
• 10: K. P. Eswaran , J. N. Gray , R. A. Lorie , I. L. Traiger, The notions of consistency and predicate locks in a database system, Communications of the ACM, v.19 n.11, p.624-633, Nov. 1976 [doi>10.1145/360363.360369]
• 11: {HA1} Hammer, M. M. and D. J. McLeod. "Semantic Integrity in a Relational Data Base Management System", Proc. of the Int. Conf. on Very Large Data Bases, 1975.
• 12: {HA2} Harel, D. "Arithmetical Completeness in Logics of Programs", MIT Laboratory for Computer Science TM-103 April 1978.
• 13: {HE1} Held, G. D., M. R. Stonebraker and E. Wong. "INGRESS--A Relational Database System", Proc. AFIPS National Computer Conf., 1975 (pp. 409-416).
• 14: {LA1} Lacroix, M. and A. Pirotte. "Domain Oriented Relational Languages", Proc. of the Int. Conf. on Very Large Data Bases, 1977 (pp. 370-378).
• 15: {LA2} Lamport, L. "Towards a Theory of Correctness for Multi-User Data Base Systems", Massachusetts Computer Associates Tech. Rep. CA-7610-0712, Oct. 1976.
• 16: Jack Minker, Search strategy and selection function for an inferential relational system, ACM Transactions on Database Systems (TODS), v.3 n.1, p.1-31, March 1978 [doi>10.1145/320241.320242]
• 17: J. M. Nicolas, First order logic formalization for functional, multivalued and mutual dependencies, Proceedings of the 1978 ACM SIGMOD international conference on management of data, May 31-June 02, 1978, Austin, Texas [doi>10.1145/509252.509269]
• 18: Susan S. Owicki, Axiomatic Proof Techniques for Parallel Programs, Cornell University, Ithaca, NY, 1975
• 19: {PA1} Papadimitriou, C. H., P. A. Bernstein and J. B. Rothnie. "Some Computational Problems Related to Database Concurrency Control", Proc. of Conf. on Theoretical Comp. Science, Waterloo, Aug. 1977 (pp. 275-282).
• 20: {PR1} Pratt, V. R. "Semantical Considerations on Floyd-Hoare Logic", Proc. of the 17th IEEE Found. of Comp. Science Conf., Oct. 1976 (pp. 109-120).
• 21: Joachim W. Schmidt, Some high level language constructs for data of type relation, ACM Transactions on Database Systems (TODS), v.2 n.3, p.247-261, Sept. 1977 [doi>10.1145/320557.320568]
• 22: {ST1} Stearns, R. E., P. M. Lewis and D. J. Rosenkrantz. "Concurrency Control for Data Base Systems", Proc. of the 17th IEEE Found. of Comp. Science Conf., Oct. 1976 (pp. 19-32).
• 23: {TH1} Thomas, R. H. "A Solution to the Update Problem for Multiple Copy Databases which Uses Distributed Control", BBN Tech. Rep. 3340, July 1975.
• 24: {VA1} van Emden, M. H. "Computational and Deductive Information Retrieval", Proc. of the IFIP Conf. of the Working Group on Formal Specifications of Prog. Lang., Aug. 1977 (pp. 17.1-17.19).
• 25: {YA1} Yasuhara, A. Recursive Function Theory and Logic, Academic Press, 1971.