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The Computer Journal 1998 41(1):1-15; doi:10.1093/comjnl/41.1.1
© 1998 by British Computer Society
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A Weakest Precondition Semantics for Z

A. Cavalcanti and J. Woodcock

Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK Email: jimw{at}comlab.ox.ac.uk

The lack of a method for developing programs from Z specifications is a widely recognized difficulty. In response to this problem, different approaches to the integration of Z with a refinement calculus have been proposed. These programming techniques are promising, but as far as we know, have not been formalized. Since they are based on refinement calculi formalized in terms of weakest preconditions, the definition of a weakest precondition semantics for Z is a significant contribution to the solution of this problem. In this paper, we actually construct a weakest precondition semantics from a relational semantics proposed by the Z standards panel. The construction provides reassurance as to the adequacy of the resulting semantics definition and additionally establishes an isomorphism between weakest preconditions and relations. Compositional formulations for the weakest precondition of some schema calculus expressions are provided.

Received November 20, 1996. revised January 9, 1998.


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