Adding Enrichments to Reened Interleavings: a New Model for the {calculus

The question of how to model {calculus name passing has attracted signiicant interest. Here, this topic is approached with a new fully abstract interleaving model. Its central feature: Every semantic object contains all its transformations under injective name replacements. It is shown how this enrichment can be used, in a systematic way, to obtain compositional interpretations of the constructors of the {calculus. The theory of non{well{founded sets serves as the mathematical basis. Moreover, category theory is used in the form of coalgebras of endo{functors. Not more is needed since transformations under name replacements are not regarded as arrows of a category of partial orders of (un{enriched) semantic objects. This approach is a hallmark of previous interleaving models of the {calculus. It seems to require a lot more category theory than is used here. Also, unlike other related work, the present one does not employ type theory.