Recasting hoare and he's unifying theory of programs in the context of general correctness

  • Authors:

  • Steve Dunne

  • Affiliations:

  • School of Computing and Mathematics, University of Teesside, Middlesbrough, UK

  • Venue:
  • IW-FM'01 Proceedings of the 5th Irish conference on Formal Methods
  • Year:
  • 2001

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Abstract

We review Hoare and He's single-predicate model of sequential programs, and uncover its inability always to provide an adequate description of the required behaviour of a sequential program which implements a partial decision procedure: a significant shortcoming in an interactive era where such programs are often found as components of reactive systems. We show how the single-predicate model can be recast to overcome this limitation, using a variation on the predicate syntactic form employed by Hoare and He for their designs, which we call a prescription. We show that our prescriptions have a remarkably simple semantic characterisation by means of a single intuitively compelling healthiness condition. Our model also admits a pleasingly simple algebraic formulation which reveals it as a natural completion of Hoare and He's model; indeed, we can show the latter to be congruent to a restricted sub-model of the former.