 Before leaving this overview of the quest for an extensional characterization of higher-order sequentiality, we should mention Bucciarelli &amp; Ehrhard (1994) who introduced a refinement of the dI-domains of Berry supporting a notion of strongly stable function which allows them to build an extensional model of PCF, which is not fully abstract. The reason for the failure of full abstraction in this case depends on the fact that PCF-definable functionals satisfy extensionality properties that fail when functions are ordered by the stable order. This was also the reason that motivated the introduction of bidomains (Berry 1978), where the stable and extensional (= pointwise) orderings of functions coexist.