Abstract (2007-02-15)

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.