A Complete Coinductive Logical System for Bisimulation Equivalence on Circular Objects

Abstract

We introduce a coinductive logical system à la Gentzen for establishing bisimulation equivalences on circular non-wellfounded regular objects, inspired by work of Coquand, and of Brandt and Henglein. In order to describe circular objects, we utilize a typed language, whose coinductive types involve disjoint sum, cartesian product, and finite powerset constructors. Our system is shown to be complete with respect to a maximal fixed point semantics. It is shown to be complete also with respect to an equivalent final semantics. In this latter semantics, terms are viewed as points of a coalgebra for a suitable endofunctor on the category Set* of non-wellfounded sets. Our system subsumes an axiomatization of regular processes, alternative to the classical one given by Milner.KeywordsCategorical SemanticType ConstructorCircular ObjectClosed TermSpringer LNCSThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.