# Quantitative Domain Theory

## Michel Schellekens

(University of Cork)

Domain Theory, an important tool to develop models for programming languages, was developed by Dana Scott in the mid-1960's. This, by now classical, theory has recently motivated active research on special purpose languages and led to interesting new applications. New models for real number computation, probabilistic computation, dataflow networks and efficiency analysis have been developed. Applications include better frameworks for exact real number computation, fractals and new techniques for integration. The main novel idea involved is the extension of Domain Theory with the concept of ``real number measures''; a field currently referred to as Quantitative Domain Theory. The use of the terminology ``quantitative'' reflects a shift from a purely order theoretic (``qualitative'' approach) to a quantified approach based on such real number measures. We present an overview of the current state of the field as well as some recent results on the development of quantitative domains.

**Tuesday 30th January 2001, 14:00**

Robert Recorde Room

Department of Computer Science