A Denotational Semantics for Total Correctness of Sequential Exact Real Programs

  • Thomas Anberrée
Conference paper

DOI: 10.1007/978-3-540-79228-4_34

Volume 4978 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Anberrée T. (2008) A Denotational Semantics for Total Correctness of Sequential Exact Real Programs. In: Agrawal M., Du D., Duan Z., Li A. (eds) Theory and Applications of Models of Computation. TAMC 2008. Lecture Notes in Computer Science, vol 4978. Springer, Berlin, Heidelberg

Abstract

We provide a domain-based denotational semantics for a sequential 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. However, for many first-order common functions \(f:{\mathbb R}^n \rightarrow {\mathbb R}\), 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 possessing a faithful denotation are not difficult to find.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Thomas Anberrée
    • 1
  1. 1.Division of Computer ScienceUniversity of Nottingham in NíngbōP.R. China