Abstract

. Coinductive characterizations of various observational congruences which arise in the semantics of -calculus, when -terms are evaluated according to various reduction strategies, are discussed. We analyze and extend to non-lazy strategies, both deterministic and nondeterministic, Howe's congruence candidate method for proving the coincidence of the applicative (bisimulation) and the contextual equivalences. This purely syntactical method is based itself on a coinductive argument. Introduction This paper is part of a general project aiming at finding elementary proof principles for reasoning rigorously on infinite computational objects, see [4, 9] for the case of higher order functions, and [8] for the case of higher order processes. In this paper, as in [4, 9], we focus on the behaviour of -terms when these are evaluated according to various reduction strategies. We address the problem of showing the coincidence of the applicative (bisimulation) equivalence with the observational ...

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