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Process algebra with guards: Combining Hoare logic with process algebra

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Formal Aspects of Computing

Abstract

We extend process algebra with guards, comparable to the guards in guarded commands or conditions in common programming constructs such as ‘if — then — else — fi’ and ‘while — do — od’.

The extended language is provided with an operational semantics based on transitions between pairs of a process and a (data-)state. The data-states are given by a data environment that also defines in which data-states guards hold and how atomic actions (non-deterministically) transform these states. The operational semantics is studied modulo strong bisimulation equivalence. For basic process algebra (without operators for parallelism) we present a small axiom system that is complete with respect to a general class of data environments. Given a particular data environmentL we add three axioms to this system, which is then again complete, provided weakest preconditions are expressible andL is sufficiently deterministic.

Then we study process algebra with parallelism and guards. A two phase-calculus is provided that makes it possible to prove identities between parallel processes. Also this calculus is complete. In the last section we show that partial correctness formulas can easily be expressed in this setting. We use process algebra with guards to prove the soundness of a Hoare logic for linear processes by translating proofs in Hoare logic into proofs in process algebra.

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Authors and Affiliations

  1. Department of Philosophy, University of Utrecht, Utrecht, The Netherlands

    Jan Friso Groote

  2. Faculty of Mathematics and Computer Science, University of Amsterdam, Kruislaan 403, 1098, SJ Amsterdam, The Netherlands

    Alban Ponse

Authors
  1. Jan Friso Groote
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  2. Alban Ponse
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Correspondence to Alban Ponse.

Additional information

Supported by ESPRIT Basic Research Action no. 3006 (CONCUR) and by RACE project no. 1046 (SPECS).

Supported by RACE project no. 1046 (SPECS).

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Groote, J.F., Ponse, A. Process algebra with guards: Combining Hoare logic with process algebra. Formal Aspects of Computing 6, 115–164 (1994). https://doi.org/10.1007/BF01221097

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