Proof-relevant pi-calculus

Roly Perera
(University of Glasgow, UK)
James Cheney
(University of Edinburgh, UK)

Formalising the pi-calculus is an illuminating test of the expressiveness of logical frameworks and mechanised metatheory systems, because of the presence of name binding, labelled transitions with name extrusion, bisimulation, and structural congruence. Formalisations have been undertaken in a variety of systems, primarily focusing on well-studied (and challenging) properties such as the theory of process bisimulation. We present a formalisation in Agda that instead explores the theory of concurrent transitions, residuation, and causal equivalence of traces, which has not previously been formalised for the pi-calculus. Our formalisation employs de Bruijn indices and dependently-typed syntax, and aligns the "proved transitions" proposed by Boudol and Castellani in the context of CCS with the proof terms naturally present in Agda's representation of the labelled transition relation. Our main contributions are proofs of the "diamond lemma" for residuation of concurrent transitions and a formal definition of equivalence of traces up to permutation of transitions.

In Iliano Cervesato and Kaustuv Chaudhuri: Proceedings Tenth International Workshop on Logical Frameworks and Meta Languages: Theory and Practice (LFMTP 2015), Berlin, Germany, 1 August 2015, Electronic Proceedings in Theoretical Computer Science 185, pp. 46–70.
Published: 27th July 2015.

ArXived at: bibtex PDF

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