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An axiomatic basis for computer programming

Published:01 January 1983Publication History
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Abstract

In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference which can be used in proofs of the properties of computer programs. Examples are given of such axioms and rules, and a formal proof of a simple theorem is displayed. Finally, it is argued that important advantages, both theoretical and practical, may follow from a pursuance of these topics.

References

  1. 1 YANOV, YU I. Logical operator schemes. Kybernetika I, (1958).Google ScholarGoogle Scholar
  2. 2 IGARASHX, S. An axiomatic approach to equivalence problems of algorithms with applications. Ph.D. Thesis 1964. Rep. Compt. Centre, U. Tokyo, 1968, pp. 1-101.Google ScholarGoogle Scholar
  3. 3 DE BAKKEa, J. W. Axiomaties of simple assignment statements. M.R. 94, Mathematiseh Centrum, Amsterdam, June 1968.Google ScholarGoogle Scholar
  4. 4 MCCARTHY, J. Towards a mathematical theory of computation. Proc. IFIP Cong. 1962, North Holland Pub. Co., Amsterdam, 1963.Google ScholarGoogle Scholar
  5. 5 BURSTALL, R. Proving properties of programs by structural induction. Experimental Programming Reports: No. 17 DMIP, Edinburgh, Feb. 1968.Google ScholarGoogle Scholar
  6. 6 VAN WIJNGAARDEN, A. Numerical analysis as an independent science. BIT 6 (1966), 66-81.Google ScholarGoogle ScholarCross RefCross Ref
  7. 7 LASET, J. Sets and other types. ALGOL Bull. 27,1968. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. 8 FLOYD, R. W. Assigning meanings to programs. Proc. Amer. Math. Soc. Symposia in Applied Mathematics, Vol. 19, pp. 19-31.Google ScholarGoogle ScholarCross RefCross Ref
  9. 9 NAUR, P. Proof of algorithms by general snapshots. BIT 6 (1966), 316-316.Google ScholarGoogle ScholarCross RefCross Ref
  10. 1 Davis, M. Computability and Unsolvability. McGraw-Hill Book Company, New York, 1958.Google ScholarGoogle Scholar
  11. 2 SAMELSONI K. Programming languages and their processing. Proceedings, IFIP Congress, 1962, North-Holland Publishing Co., Amsterdam, 1963, p. 487.Google ScholarGoogle Scholar

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