# zbMATH — the first resource for mathematics

Formalising the $$\pi$$-calculus using nominal logic. (English) Zbl 1168.68436
Seidl, Helmut (ed.), Foundations of software science and computational structures. 10th international conference, FOSSACS 2007, held as part of the joint European conferences on theory and practice of software, ETAPS 2007, Braga, Portugal, March 24 – April 1, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-71388-3/pbk). Lecture Notes in Computer Science 4423, 63-77 (2007).
Summary: We formalise the pi-calculus using the nominal datatype package, a package based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics in order to conduct machine checkable proofs, closely following the intuitive arguments found in manual proofs. In this way we have covered many of the standard theorems of bisimulation equivalence and congruence, both late and early, and both strong and weak in a unison manner. We thus provide one of the most extensive formalisations of a process calculus ever done inside a theorem prover.
A significant gain in our formulation is that agents are identified up to alpha-equivalence, thereby greatly reducing the arguments about bound names. This is a normal strategy for manual proofs about the pi-calculus, but that kind of hand waving has previously been difficult to incorporate smoothly in an interactive theorem prover. We show how the nominal logic formalism and its support in Isabelle accomplishes this and thus significantly reduces the tedium of conducting completely formal proofs. This improves on previous work using weak higher order abstract syntax since we do not need extra assumptions to filter out exotic terms and can keep all arguments within a familiar first-order logic.
For the entire collection see [Zbl 1116.68009].

##### MSC:
 68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) 68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
Isabelle/HOL
Full Text: