A Fully Abstract Model for the π - calculus

This paper provides both a fully abstract (domain-theoretic) model for the π -calculus and a universal (set-theoretic) model for the finite π -calculus with respect to strong late bisimulation and congruence. This is done by considering categorical models, defining a metalanguage for these models, and translating the π -calculus into the metalanguage. A technical novelty of our approach is an abstract proof of full abstraction: The result on full abstraction for the finite π -calculus in the set-theoretic model is axiomatically extended to the whole π -calculus with respect to the domain-theoretic interpretation. In this proof, a central role is played by the description of nondeterminism as a free construction and by the equational theory of the metalanguage. C © 2002 Elsevier Science (USA)