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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramsky, S., Jung, A.: Domain theory. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. 3, pp. 1–168. Clarendon Press (1994)
Boehm, H.J., Cartwright, R.: Exact real arithmetic: Formulating real numbers as functions. In: Research topics in functional programming, pp. 43–64. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA (1990)
Escardó, M.H.: PCF extended with real numbers: A domain-theoretic approach to higher-order exact real number computation. PhD thesis, Department of Computing, Imperial College, University of London (1996)
Farjudian, A.: Sequentiality in Real Number Computation. PhD thesis, School of Computer Science, University of Birmingham (2004)
Di Gianantonio, P.: A Functional Approach to Computability on Real Numbers. PhD thesis, University of Pisa, Udine (1993)
Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S.: Continuous Lattices and Domains. Encyclopedia of Mathematics and its Applications, vol. 93. Cambridge University Press, Cambridge (2003)
Marcial-Romero, J.R.: Semantics of a Sequential Language for Exact Real-Number Computation. PhD thesis, School of Computer Science, University of Birmingham U.K. (2004)
Marcial-Romero, J.R., Escardó, M.H.: Semantics of a sequential language for exact real-number computation. Theoretical Computer Science 379(1-2), 120–141 (2007)
Plotkin, G.D.: LCF considered as a programming language. Theor. Comput. Sci. 5(3), 225–255 (1977)
Streicher, T.: Domain-Theoretic Foundations of Functional Programming. Imperial College Press, London (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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. https://doi.org/10.1007/978-3-540-79228-4_34
Download citation
DOI: https://doi.org/10.1007/978-3-540-79228-4_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79227-7
Online ISBN: 978-3-540-79228-4
eBook Packages: Computer ScienceComputer Science (R0)