A Construction of Typed Lambda Models Related to Feasible Computability

In this paper we develop an approach to the notion of computable functionals in a very abstract setting not restricted to Turing or, say, polynomial computability. We assume to start from some basic class of domains and a basic class of functions deened on these domains. (An example may be natural numbers with polytime computable functions). Then we deene what are \all" corresponding functionals of higher types which add nothing new to these basic functions. We call such functionals computable or, more technically and adequately speaking, substitutable. (Similarly, in D.Scott's domains we say about continuous functionals as about far-reaching abstraction of computable ones.) Our results are applicable to quite arbitrary (complexity) classes of functions, satisfying a very general Assumption.