Semantics, Specification Logic, and Hoare Logic of Exact Real Computation
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| Publicado en: | arXiv.org (Jun 21, 2024), p. n/a |
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| Autor principal: | |
| Otros Autores: | , , , , , , , , |
| Publicado: |
Cornell University Library, arXiv.org
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| Materias: | |
| Acceso en línea: | Citation/Abstract Full text outside of ProQuest |
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| Resumen: | We propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides a formal programming language-theoretic foundation to the algorithmic processing of real numbers. In order to capture multi-valuedness, which is well-known to be essential to real number computation, we use a Plotkin powerdomain and make our programming language semantics computable and complete: all and only real functions computable in computable analysis can be realized in ERC. The base programming language supports real arithmetic as well as implicit limits; expansions support additional primitive operations (such as a user-defined exponential function). By restricting integers to Presburger arithmetic and real coercion to the `precision' embedding \(\mathbb{Z}\ni p\mapsto 2^p\in\mathbb{R}\), we arrive at a first-order theory which we prove to be decidable and model-complete. Based on said logic as specification language for preconditions and postconditions, we extend Hoare logic to a sound (w.r.t. the denotational semantics) and expressive system for deriving correct total correctness specifications. Various examples demonstrate the practicality and convenience of our language and the extended Hoare logic. |
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| ISSN: | 2331-8422 |
| DOI: | 10.46298/lmcs-20(2:17)2024 |
| Fuente: | Engineering Database |