PROJECTING SEQUENTIAL ALGORITHMS ON STRONGLY STABLE FUNCTIONS

We relate two sequential models of PCF: the sequential algorithm model due to Berry and Curien and the strongly stable model due to Bucciare lli and the author. More precisely, we show that all the morphisms ara ising in the strongly stable model of PCF are sequential in the sense that they are the ''extensional projections'' of some sequential algor ithms. We define a model of PCF where morphisms are ''extensional'' se quential algorithms and prove that any equation between PCF terms whic h holds in this model also holds in the strongly stable model.