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A Denotational Semantics for Total Correctness of Sequential Exact Real Programs.
 

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 domain-based denotational semantics for a se-
quential language for exact real number computation, equipped with a
non-deterministic 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 first-order 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

  

Source: Anberrée, Thomas - School of Computer Science, University of Nottingham Ningbo, China

 

Collections: Computer Technologies and Information Sciences