Process algebra with guards: Combining Hoare logic with process algebra

Abstract

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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Index Terms

• Computing methodologies

  • Symbolic and algebraic manipulation

• Software and its engineering

  • Software notations and tools

    • General programming languages

• Theory of computation

  • Formal languages and automata theory

    • Formalisms

  • Logic

  • Semantics and reasoning

    • Program semantics