Formalising the pi-calculus using nominal logic

Abstract

We formalise the pi-calculus using the nominal datatype package, based onideas from the nominal logic by Pitts et al., and demonstrate an implementationin Isabelle/HOL. The purpose is to derive powerful induction rules for thesemantics in order to conduct machine checkable proofs, closely following theintuitive arguments found in manual proofs. In this way we have covered many ofthe standard theorems of bisimulation equivalence and congruence, both late andearly, and both strong and weak in a uniform manner. We thus provide one of themost extensive formalisations of a process calculus ever done inside a theoremprover. A significant gain in our formulation is that agents are identified up toalpha-equivalence, thereby greatly reducing the arguments about bound names.This is a normal strategy for manual proofs about the pi-calculus, but thatkind of hand waving has previously been difficult to incorporate smoothly in aninteractive theorem prover. We show how the nominal logic formalism and itssupport in Isabelle accomplishes this and thus significantly reduces the tediumof conducting completely formal proofs. This improves on previous work usingweak higher order abstract syntax since we do not need extra assumptions tofilter out exotic terms and can keep all arguments within a familiarfirst-order logic.Comment: 36 pages, 3 figure