A combinatory algebra for sequential functionals of finite type

Abstract

It is shown that the type structure of nite-type functionals associated to a combinatory algebra of partial functions from IN to IN (in the same way as the type structure of the countable functionals is associated to the partial combinatory algebra of total functions from IN to IN), is isomorphic to the type structure generated by object N (the at domain on the natural numbers) in Ehrhard's category of \dI-domains with coherence", or his \hypercoherences".