*Abstract:*

We consider a notion of sequential functional of finite type,
more generous than the familiar notion embodied in Plotkin's
language PCF. We study both the ``full'' and ``effective'' partial
type structures arising from this notion of sequentiality. The full
type structure coincides with that given by the *strongly
stable* model of Bucciarelli and Ehrhard; it has also been
characterized by van Oosten in terms of realizability over a
certain combinatory algebra.

We survey and relate several known characterizations of these
type structures, and obtain some new ones. We show that (in both
the full and effective scenarios) every finite type can be obtained
as a retract of the pure type 2, and hence that all elements of the
effective type structure are definable in PCF extended by a certain
*universal* functional *H*. We also consider the
relationship between our notion of sequentially computable
functional and other known notions of higher-type
computability.

**ECS-LFCS-98-402**.

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