A fully abstract denotational semantics for the π-calculus

This paper describes the construction of two set-theoretic denotational models for the π-calculus. The models are obtained as initial solutions to domain equations in a functor category. By associating with each syntactic construct of the π-calculus a natural transformation over these models we obtain two interpretations for the language. We also show that these models are fully abstract with respect to natural behavioural preorders over terms in the language. By this we mean that two terms are related behaviourally if and only if their interpretations in the model are related. The behavioural preorders are the standard versions of may and must testing adapted to the π-calculus