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Formal Proof of Soundness for an RL Prover

Andrei Arusoaie 1 David Nowak 2 Vlad Rusu 1 Dorel Lucanu 3
1 DREAMPAL - Dynamic Reconfigurable Massively Parallel Architectures and Languages
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 2XS - Extra Small Extra Safe
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : Proving programs correct is one of the major challenges that computer scientists have been struggling with during the last decades. For this purpose, Reachability Logic (RL) was proposed as a language-parametric generalisation of Hoare Logic. Recently, based on RL, an automatic verification procedure was given and proved sound. In this paper we generalise this procedure and prove its soundness formally in the Coq proof assistant. For the formalisation we had to deal with all the minutiae that were neglected in the paper proof. The trickiest one was appropriate renaming of free variables which, we discovered, was handled in the paper proof using an insufficient assumption. We also discovered a missing case in the paper proof, and we clarified some implicit and hidden hypotheses. Last but not least, the Coq formalisation provides us with a certified program-verification procedure.
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https://hal.inria.fr/hal-01244578
Contributor : Pal Dream <>
Submitted on : Tuesday, December 15, 2015 - 11:50:13 PM
Last modification on : Friday, December 11, 2020 - 6:44:06 PM
Long-term archiving on: : Saturday, April 29, 2017 - 3:58:52 PM

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  • HAL Id : hal-01244578, version 1

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Andrei Arusoaie, David Nowak, Vlad Rusu, Dorel Lucanu. Formal Proof of Soundness for an RL Prover. [Technical Report] RR-0471, INRIA Lille - Nord Europe; Alexandru Ioan Cuza, University of Iasi. 2015, pp.27. ⟨hal-01244578⟩

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