Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof

In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the large-scale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more than a decade of CPU time and produced 27 GB of proof witnesses. The checker uses an untrusted oracle based on these witnesses and is able to verify the smaller case of 8 inputs within a couple of days, but it did not scale to the full proof for 9 inputs. In this paper, we describe several non-trivial optimizations of the algorithm in the checker, obtained by appropriately changing the formalization and capitalizing on the symbiosis with an adequate implementation of the oracle. We provide experimental evidence of orders of magnitude improvements to both runtime and memory footprint for 8 inputs, and actually manage to check the full proof for 9 inputs.Comment: IMADA-preprint-c

TRX: A Formally Verified Parser Interpreter

Parsing is an important problem in computer science and yet surprisingly little attention has been devoted to its formal verification. In this paper, we present TRX: a parser interpreter formally developed in the proof assistant Coq, capable of producing formally correct parsers. We are using parsing expression grammars (PEGs), a formalism essentially representing recursive descent parsing, which we consider an attractive alternative to context-free grammars (CFGs). From this formalization we can extract a parser for an arbitrary PEG grammar with the warranty of total correctness, i.e., the resulting parser is terminating and correct with respect to its grammar and the semantics of PEGs; both properties formally proven in Coq.Comment: 26 pages, LMC

Permanent Polymer Coating for in vivo MRI Visualization of Tissue Reinforcement Prostheses

The clinical advantage of MRI visualization of prostheses in soft tissue prolapses is very appealing as over 1?000?000 MRI-transparent synthetic meshes are implanted annually, and postoperative complications such as mesh shrinkage and migration are frequent. Here, the synthesis of a new material composed of a DTPA-Gd complex grafted onto a backbone of PMA via a covalent bond is described (DTPA-Gd-PMA). This new polymer is sprayed onto meshes and gives an MR signal for a long period without any significant release of Gd. In vitro cytocompatibility tests on fibroblasts show limited cytotoxicity. Microscopic investigations indicate that vital cells rapidly colonize the material. Finally, coated meshes implanted in rats are easily recognizable using an MR imaging system

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

Conception de prothèse visible en IRM pour la prise en charge chirurgicale des prolapsus génitaux et des hernies abdominales

National audienc

Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of a C Program

We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.Comment: No. RR-7826 (2011

Roadless wilderness area determines forest elephant movements in the Congo Basin

A dramatic expansion of road building is underway in the Congo Basin fuelled by private enterprise, international aid, and government aspirations. Among the great wilderness areas on earth, the Congo Basin is outstanding for its high biodiversity, particularly mobile megafauna including forest elephants (Loxodonta africana cyclotis). The abundance of many mammal species in the Basin increases with distance from roads due to hunting pressure, but the impacts of road proliferation on the movements of individuals are unknown. We investigated the ranging behaviour of forest elephants in relation to roads and roadless wilderness by fitting GPS telemetry collars onto a sample of 28 forest elephants living in six priority conservation areas. We show that the size of roadless wilderness is a strong determinant of home range size in this species. Though our study sites included the largest wilderness areas in central African forests, none of 4 home range metrics we calculated, including core area, tended toward an asymptote with increasing wilderness size, suggesting that uninhibited ranging in forest elephants no longer exists. Furthermore we show that roads outside protected areas which are not protected from hunting are a formidable barrier to movement while roads inside protected areas are not. Only 1 elephant from our sample crossed an unprotected road. During crossings her mean speed increased 14-fold compared to normal movements. Forest elephants are increasingly confined and constrained by roads across the Congo Basin which is reducing effective habitat availability and isolating populations, significantly threatening long term conservation efforts. If the current road development trajectory continues, forest wildernesses and the forest elephants they contain will collapse