A Denotational Semantics for Total Correctness of Sequential Exact Real Programs

* Final gross prices may vary according to local VAT.

Get Access

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.