On domain algebras

Achim Jung

(University of Birmingham)

Domains (in the sense of Dana Scott) can be characterised via
their order structure or via their (Scott) topology. A lot is known
about their structural properties both at the individual and the
categorical level. In applications, in addition to the order structure
some algebraic operations satisfying certain equations are often
required. The interplay between order/topology and algebra is not
entirely straightforward but we do now have some general existence theorems.

In this talk I intend to present the various approaches to domain theory
that one might be interested in from an applications point of view, and
then explain the difficulties one has to overcome if one is trying to
add algebraic structure. In joint work with M. A. Moshier and S.
Vickers, we have found a new way of constructing domain algebras which
is much more concrete than the method that was employed before. More
recently still, K. Keimel and J. Lawson discovered that this can be
explained and extended very elegantly by replacing order with topology.
Tuesday 17th November 2009, 14:00
Robert Recorde Room
Department of Computer Science