A denotational semantics for total correctness of sequential exact real programs

Authors:
Thomas Anberrée
Affiliations:
Division of Computer Science, University of Nottingham in Níngbō, P.R. China
Venue:
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Year:
2008

Citing 4
Cited 1

Exact real arithmetic formulating real numbers as functions

Research topics in functional programming
Domain theory

Handbook of logic in computer science (vol. 3)
Domain-theoretic Foundations of Functional Programming

Domain-theoretic Foundations of Functional Programming
Semantics of a sequential language for exact real-number computation

Theoretical Computer Science

First-Order Universality for Real Programs

CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice

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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 : 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 possessing a faithful denotation are not difficult to find.