Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
A calculus of mobile processes, II
Information and Computation
Metamathematics, machines, and Go¨del's proof
Metamathematics, machines, and Go¨del's proof
&pgr;-calculus in (Co)inductive-type theory
Theoretical Computer Science - Special issues on models and paradigms for concurrency
A Full Formalisation of pi-Calculus Theory in the Calculus of Constructions
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Journal of Functional Programming
Formalising the π-calculus using nominal logic
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
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We use the interactive theorem prover Isabelle to prove that the algebraic axiomatization of bisimulation equivalence in the pi-calculus is sound and complete. This is the first proof of its kind to be wholly machine checked. Although the result has been known for some time the proof had parts which needed careful attention to detail to become completely formal. It is not that the result was ever in doubt; rather, our contribution lies in the methodology to prove completeness and get absolute certainty that the proof is correct, while at the same time following the intuitive lines of reasoning of the original proof. Completeness of axiomatizations is relevant for many variants of the calculus, so our method has applications beyond this single result. We build on our previous effort of implementing a framework for the pi-calculus in Isabelle using the nominal data type package, and strengthen our claim that this framework is well suited to represent the theory of the pi-calculus, especially in the smooth treatment of bound names.