 
Summary: On the nonsequential nature of
domain models of realnumber computation
Thomas AnberrŽee 1
School of Computer Science
Birmingham University
Birmingham, U.K.
Abstract
EscardŽo, Hofmann and Streicher showed that realnumber computations in the intervaldomain environment
are inherently parallel, in the sense that they imply the presence of weak parallelor. Part of the argument
involves showing that the addition operation is not Vuilemin sequential. We generalize this to all continuous
domain environments for the real line. The key property of the real line that leads to this phenomenon is
its connectedness. We show that any continuous domain environment for any connected topological space
exhibits a similar parallel effect.
Keywords: domain theory, real number computation, sequentiality, connectedness
1 Introduction
EscardŽo, Hofmann and Streicher [4] investigated the possibility of sequential com
putation on the real line via its well known intervaldomain environment, considered
by e.g. Edalat [2] and EscardŽo [3]. The main result of [4] is that sequential com
putation on the reals via the interval domain is extremely restrictive, to the extent
that not even a basic operation such as addition is sequential. The argument in [4]
