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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.

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V. Brattka (1996) Recursive characterization of computable real-valued functions and relations. Theoretical Computer Science 162 4577.

J. Marcial-Romero and M. Escardó (2007) Semantics of a sequential language for exact real-number computation. Theoretical Computer Science 379 (1–2) 120141.

G. Plotkin (1977) LCF considered as a programming language. Theoretical Computer Science 5 (3) 225255.

T. Streicher (2006) Domain-Theoretic Foundations of Functional Programming, World Scientific.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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