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Assigning Meanings to Programs

  • Robert W. Floyd
Chapter
Part of the Studies in Cognitive Systems book series (COGS, volume 14)

Abstract

This paper attempts to provide an adequate basis for formal definitions of the meanings of programs in appropriately defined programming languages, in such a way that a rigorous standard is established for proofs about computer programs, including proofs of correctness, equivalence, and termination. The basis of our approach is the notion of an interpretation of a program: that is, an association of a proposition with each connection in the flow of control through a program, where the proposition is asserted to hold whenever that connection is taken. To prevent an interpretation from being chosen arbitrarily, a condition is imposed on each command of the program. This condition guarantees that whenever a command is reached by way of a connection whose associated proposition is then true, it will be left (if at all) by a connection whose associated proposition will be true at that time. Then by induction on the number of commands executed, one sees that if a program is entered by a connection whose associated proposition is then true, it will be left (if at all) by a connection whose associated proposition will be true at that time. By this means, we may prove certain properties of programs, particularly properties of the form: ‘If the initial values of the program variables satisfy the relation R l, the final values on completion will satisfy the relation R 2’.

Keywords

Free Variable Assignment Statement Deductive System Statement List Verification Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    McCarthy, J.: 1963, ‘A Basis for a Mathematical Theory of Computation’, in Computer Programming and Formal Systems, North-Holland, Amsterdam, pp. 33–70.CrossRefGoogle Scholar
  2. 2.
    McCarthy, J.: 1962, ‘Towards a Mathematical Science of Computation’, Proc. IFIP Congr. 62, North Holland, Amsterdam, pp. 21–28.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Robert W. Floyd
    • 1
  1. 1.Carnegie Institute of TechnologyPittsburghUSA

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