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’.
- 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.
This work was supported by the Advanced Research Projects Agency of the Office of the Secretary of Defense (SD-146).
This is a preview of subscription content, access via your institution.
Tax calculation will be finalised at checkout
Purchases are for personal use onlyLearn about institutional subscriptions
Unable to display preview. Download preview PDF.
McCarthy, J.: 1963, ‘A Basis for a Mathematical Theory of Computation’, in Computer Programming and Formal Systems, North-Holland, Amsterdam, pp. 33–70.
McCarthy, J.: 1962, ‘Towards a Mathematical Science of Computation’, Proc. IFIP Congr. 62, North Holland, Amsterdam, pp. 21–28.
Editors and Affiliations
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Floyd, R.W. (1993). Assigning Meanings to Programs. In: Colburn, T.R., Fetzer, J.H., Rankin, T.L. (eds) Program Verification. Studies in Cognitive Systems, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1793-7_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4789-0
Online ISBN: 978-94-011-1793-7
eBook Packages: Springer Book Archive