Lazy functions and mobile processes

This paper continues the study of Milner's encoding of the lazy-calculus into the-calculus Mil90]. The encoding is shown to give rise to a-model in which, in accordance with the theory of the lazy-calculus, conditional extensionality holds. However, the model is not fully abstract. To obtain full abstraction, the operational equivalence on-terms (applicative bisimulation) is reened. The new relation, called open applicative bisimulation, allows us to observe some internal structure of-terms, and coincides with the L evy-Longo Tree equality. Milner's encoding is presented on a sublanguage of the-calculus similar to those proposed by Boudol Bou92], Honda and Tokoro HT92]. Some properties of bisimulation on this sublanguage are demonstrated and used to simplify a few proofs in the paper. For instance, ground bisimulation, a form of bisimulation where no name instantiation on input actions is required, is proved to be a congruence relation; as a corollary, various-calculus bisimilarity equivalences (ground, late, early, open) are shown to coincide on this sublanguage. Fonctions lazy et processus mobiles R esum e : Cet article reprend l' etude de Milner sur l'encobdage du lazy-calculus en-calculus Mil90]. Il d emontre que l'encodage d etermine un-mod ele pour lequel, conform e-ment a la th eorie de lazy-calculus l'extensionalit e conditionelle vaut. Toutefois, le mod ele n'est pas \fully abstract". Pour obtenir une \fully abstraction", l' equivalence op erationelle sur les-termes (bisimulation applicative) est aan ee. La nouvelle relation, appel ee bisimu-lation applicative ouverte, permet d'observer certaines structures internes de-termes, et coincide avec l' egalit e des arbres de L evy-Longo. L'encodage de Milner est pr esent e sur un sous-langage de-calculus, similaire a ceux propos es par Boudol Bou92], Honda et Tokoro HT92]. Certaines propri et es de la bisimula-tion sur ce sous-langage sont d emontr ees et utilis ees pour simpliier quelques d emonstrations dans cet article. Par exemple, nous d emontrons que la ground bisimulation, une forme de bisimulation pour laquelle aucune instantiation de nom sur les actions d'input n'est requise, est une relation de congruence ; comme corollaire, diverses equivalences de bisimilarit e de-calculus (ground, late, early, open) coincident egalement sur ce sous-langage.