Abstract

We present a cartesian closed category of dI-domains with coherence and strongly stable functions which provides a new model of PCF, where terms are interpreted by functions and where, at first order, all functions are sequential. We show how this model can be refined in such a way that the theory it induces on the terms of PCF be strictly finer than the theory induced by the Scott model of continuous functions. Keywords: lambda-calculus, denotational semantics, continuity, stability, sequentiality. This article is published in Information and Computation 110(1994), pp. 265-296. 1 Contents 1 dI-domains and stable functions 3 2 From sequentiality to strong stability 6 3 Strong stability 10 4 Extensionality 16 5 Extensionally Embedded dI-Domains with Coherence 18 6 About the theory induced by ESS on PCF 23

Citations