Specification and refinement in general correctness

  • Authors:

  • Steve Dunne;Andy Galloway;Bill Stoddart

  • Affiliations:

  • School of Computing and Mathematics, University of Teesside;High Integrity Systems Engineering Group, University of York;School of Computing and Mathematics, University of Teesside

  • Venue:
  • 3FACS'98 Proceedings of the 3rd BCS-FACS conference on Northern Formal Methods
  • Year:
  • 1998

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Abstract

We augment B's existing total-correctness semantics of weakest precondition (wp) with a partial-correctness semantics of weakest liberal precondition (wlp). By so doing we achieve a general-correctness semantics for B operations which not only accords more fully with our natural computational intuition, but also extends the essential expressive capability of B's Generalised Substitution Language (GSL) to embrace a whole new class of operations called semi-decidable, whose behaviour cannot be characterised in terms of total correctness alone. The ability to specify semi-decidable operations is important because a desired conventional operation may lend itself to implementation as a concurrent federation of semi-decidable operations co-operating under a mutual "termination pact". Indeed, computational constraints may render this the only viable implementation strategy. We call a generalised substitution invested with our general-correctness semantics an abstract command. Our Abstract Command Language (ACL) is thus syntactically indistinguishable from the GSL, save for the introduction of one new composition operator, concert, expressing a "termination pact" between two concurrent abstract commands.