 
Summary: A Denotational Semantics for Total Correctness
of Sequential Exact Real Programs.
Thomas Anberr´ee
Division of Computer Science, University of Nottingham in N´ingb¯o, PR China
Thomas.Anberree@nottingham.edu.cn
Abstract. We provide a domainbased denotational semantics for a se
quential language for exact real number computation, equipped with a
nondeterministic test operator. The semantics is only an approximate
one, because the denotation of a program for a real number may not be
precise enough to tell which real number the program computes. How
ever, for many firstorder common functions f : Rn
R, there exists
a program for f whose denotation is precise enough to show that the
program indeed computes the function f. In practice such programs pos
sessing a faithful denotation are not difficult to find.
1 Introduction
We provide a denotational model for a functional programming language for
exact real number computation. A well known difficulty in real number com
putation is that the tests x = y and x y are undecidable and hence cannot
be used to control the execution flow of programs. One solution, proposed by
