Skip to main content Accessibility help

Semantical proofs of correctness for programs performing non-deterministic tests on real numbers


We consider a functional language that performs non-deterministic tests on real numbers and define a denotational semantics for that language based on Smyth powerdomains. 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 total functions f : n, there exists a program for f whose denotation is precise enough to show that the program indeed computes the function f. In practice, it is not difficult to find programs like this that possess a faithful denotation. We provide a few examples of such programs and the corresponding proofs of correctness.

Hide All
Abramsky, S. and Jung, A. (1994) Domain theory. In: Abramsky, S., Gabbay, D. M. and Maibaum, T. S. E. (eds.) Handbook of Logic in Computer Science 3, Clarendon Press 1168.
Anberree, T. (2007) A denotational semantics for total correctness of sequential exact real programs, Ph.D. thesis, The University of Birmingham, United Kingdom.
Boehm, H. and Cartwright, R. (1990) Exact real arithmetic: formulating real numbers as functions. In: Research topics in functional programming, Addison-Wesley Longman 4364.
Brattka, V. (1996) Recursive characterization of computable real-valued functions and relations. Theoretical Computer Science 162 4577.
Gierz, G., Hofmann, K., Keimel, K., Lawson, J., Mislove, M. and Scott, D. (2003) Continuous Lattices and Domains. Encyclopedia of Mathematics and its Applications, Cambridge University Press 93.
Marcial-Romero, J. (2004) Semantics of a sequential language for exact real-number computation, Ph.D. thesis, The University of Birmingham, United Kingdom.
Marcial-Romero, J. and Escardó, M. (2007) Semantics of a sequential language for exact real-number computation. Theoretical Computer Science 379 (1–2)120141.
Plotkin, G. (1977) LCF considered as a programming language. Theoretical Computer Science 5 (3)225255.
Streicher, T. (2006) Domain-Theoretic Foundations of Functional Programming, World Scientific.
Weihrauch, K. (2000) Computable analysis: an introduction, Springer-Verlag.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed