# Computing Total, Computable Functionals

Dag Normann Department of Mathematics University of Oslo 4pm Monday 15 February 1999 Room 2511, JCMB, King's Buildings Dag will be visiting on Monday only, hosted by Martin Escardo.

We will consider the typed hierarchy of algebraic domains based on the flat domain representation of the natural numbers. We prove that to any total, computable functional of type three there is a total functional below it definable via a deterministic algorithm. This algorithm can be realised as a PCF-program. If time, we will discuss how this result extends to higher types.