The finite pi-calculus has an explicit set-theoretic functor-category model that is known to be fully abstract for strong late bisimulation congruence. We characterize this as the initial free algebra for an appropriate set of operations and equations in the enriched Lawvere theories of Plotkin and Power. Thus we obtain a novel algebraic description for models of the pi-calculus, and validate an existing construction as the universal such model.
The algebraic operations are intuitive, covering name creation, communication of names over channels, and nondeterminism; the equations then combine these features in a modular fashion. We work in an enriched setting, over a "possible worlds" category of sets indexed by available names. This expands significantly on the classical notion of algebraic theories, and in particular allows us to use nonstandard arities that vary as processes evolve.
Based on our algebraic theory we describe a category of models for the pi-calculus, and show that they all preserve bisimulation congruence. We develop a direct construction of free models in this category; and generalise previous results to prove that all free-algebra models are fully abstract.
|Title of host publication||Foundations of Software Science and Computational Structures|
|Place of Publication||Berlin|
|Number of pages||15|
|Publication status||Published - 2005|
|Event||8th International Conference on Foundations of Software Science and Computation Structures - Edinburgh|
Duration: 4 Apr 2005 → 8 Apr 2005
|Name||Lecture Notes in Computer Science|
|Publisher||Springer Berlin / Heidelberg|
|Conference||8th International Conference on Foundations of Software Science and Computation Structures|
|Period||4/04/05 → 8/04/05|