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The co-invariant generator: An aid in deriving loop bodies

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Formal Aspects of Computing

Abstract

Given a loop invariant,I, and an assignment,α, which decreases the variant, we define a constructive function, cg, called the co-invariant generator, which has the property thatIΛ cg (α, I) ⇒ wp (α, I), where wp (α, I) is the weakest precondition forα to establish I. Several results about the co-invariant generator are proved, important special cases are considered, and a non-trivial example of its use in deriving the body of a loop is given. We also define a function which performs a related constructive action on terms formed from binary operations. The coinvariant generator makes a useful contribution to formalising and automating a key step in program derivation.

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References

  1. Backhouse, R. C.:Program Construction and Verification, Prentice Hall, London, 1986.

    Google Scholar 

  2. Dijkstra, E. W.:A Discipline of Programming, Prentice-Hall, Englewood Cliffs, N.J. 1976.

    MATH  Google Scholar 

  3. Dijkstra, E. W. and Feijen, W. H. J.:A Method of Programming, Addison-Wesley, Wokingham, England, 1988.

    MATH  Google Scholar 

  4. Dromey, R. G.: Derivation of Sorting Algorithms from a Specification.The Computer Journal,30, 512–518 (1987).

    Article  MATH  Google Scholar 

  5. Dromey, R. G.:Program Derivation, Addison-Wesley, Sydney, 1989.

    MATH  Google Scholar 

  6. Dromey, R. G. and Billington, D.: Stepwise Program Derivation. Research Report43, School of Computing and Information Technology, Griffith University, Nathan, Brisbane, Queensland, 4111, Australia, 1991

    Google Scholar 

  7. Enderton, H. B.:Elements of Set Theory, Academic Press, Orlando, 1977.

    MATH  Google Scholar 

  8. Fitting, M.:First-Order Logic and Automated Theorem Proving, Springer-Verlag, New York, 1990.

    Book  MATH  Google Scholar 

  9. Gries, D.:The Science of Programming, Springer-Verlag, New York, 1981.

    Book  MATH  Google Scholar 

  10. Gries, D.: A Note on a Standard Strategy for Developing Loop Invariants and Loops.Science of Computer Programming,2, 207–217 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  11. Kaldewaij, A.:Programming: The Derivation of Algorithms, Prentice Hall, New York, 1990.

    Google Scholar 

  12. Nerode, A. and Shore, R. A.:Logic for Applications, Springer-Verlag, New York, 1993.

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Computing and Information Technology, Griffith University, Nathan, 4111, Brisbane, Queensland, Australia

    David Billington & R. Geoff Dromey

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  1. David Billington
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  2. R. Geoff Dromey
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Correspondence to David Billington.

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Billington, D., Dromey, R.G. The co-invariant generator: An aid in deriving loop bodies. Formal Aspects of Computing 8, 108–126 (1996). https://doi.org/10.1007/BF01211053

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