A First Order Coalgebraic Model of PiCalculus Early Observational Equivalence Marzia Buscemi and Ugo Montanari
In this paper, we propose a compositional coalgebraic semantics of the
picalculus based on a novel approach for lifting calculi with
structural axioms to coalgebraic models. We equip the transition
system of the calculus with permutations, parallel composition and
restriction operations, thus obtaining a bialgebra. No prefix
operation is introduced, relying instead on a clause format defining
the transitions of recursively defined processes. The unique morphism
to the final bialgebra induces a bisimilarity relation which coincides
with observational equivalence and which is a congruence with respect
to the operations. The permutation algebra is enriched with a name
extrusion operator delta 'a la De Brujin, that shifts any name to the
successor and generates a new name in the first variable x0. As a
consequence, in the axioms and in the SOS rules there is no need to
refer to the support, i.e., the set of significant names, and, thus,
the model turns out to be first order.

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