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Gilbert G.,ENS Lyon
CPP 2017 - Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs, co-located with POPL 2017 | Year: 2017

Cauchy reals can be defined as a quotient of Cauchy sequences of rationals. In this case, the limit of a Cauchy sequence of Cauchy reals is defined through lifting it to a sequence of Cauchy sequences of rationals. This lifting requires the axiom of countable choice or excluded middle, neither of which is available in homotopy type theory. To address this, the Univalent Foundations Program uses a higher inductive-inductive type to define the Cauchy reals as the free Cauchy complete metric space generated by the rationals. We generalize this construction to define the free Cauchy complete metric space generated by an arbitrary metric space. This forms a monad in the category of metric spaces with Lipschitz functions. When applied to the rationals it defines the Cauchy reals. Finally, we can use Altenkirch and Danielson (2016)'s partiality monad to define a semi-decision procedure comparing a real number and a rational number. © 2017 ACM.

News Article | February 27, 2017
Site: phys.org

The mystery that is the origin of flowering plants has been partially solved thanks to a team from the Laboratoire de Physiologie Cellulaire et Végétale (CNRS/Inra/CEA/Université Grenoble Alpes), in collaboration with the Reproduction et Développement des Plantes laboratory (CNRS/ENS Lyon/Inra/Université Claude Bernard Lyon 1) and Kew Gardens (UK). Their discovery, published in the journal New Phytologist on February 24, 2017, sheds light on a question that much intrigued Darwin: the appearance of a structure as complex as the flower over the course of evolution. Terrestrial flora is today dominated by flowering plants. They provide our food and contribute color to the plant world. But they have not always existed. While plants colonized the land over 400 million years ago, flowering plants appeared only 150 million years ago. They were directly preceded by a group known as the gymnosperms, whose mode of reproduction is more rudimentary and whose modern-day representatives include conifers. Darwin long pondered the origin and rapid diversification of flowering plants, describing them as an "abominable mystery". In comparison with gymnosperms, which possess rather rudimentary male and female cones (like the pine cone), flowering plants present several innovations: the flower contains the male organs (stamens) and the female organs (pistil), surrounded by petals and sepals, while the ovules, instead of being naked, are protected within the pistil. How was nature able to invent the flower, a structure so different from that of cones? The team led by François Parcy, a CNRS senior researcher at the Cell and Plant Physiology Laboratory (CNRS/Inra/CEA/Université Grenoble Alpes), has just provided part of the answer. To do so, the researchers studied a rather original gymnosperm called Welwitschia mirabilis. This plant, which can live for more than a millennium, grows in the extreme conditions of the deserts of Namibia and Angola, and, like other gymnosperms, possesses separate male and female cones. What is exceptional is that the male cones possess a few sterile ovules and nectar, which indicates a failed attempt to invent the bisexual flower. Yet, in this plant (as well as in certain conifers), the researchers found genes similar to those responsible for the formation of flowers, and which are organized according to the same hierarchy (with the activation of one gene activating the next gene, and so on)! The fact that a similar gene cascade has been found in flowering plants and their gymnosperm cousins indicates that this is inherited from their common ancestor. This mechanism did not have to be invented at the time of the origins of the flower: it was simply inherited and reused by the plant, a process that is often at work in evolution. The study of the current biodiversity of plants thus enables us to go back in time and gradually sketch the genetic portrait of the common ancestor of a large proportion of modern-day flowers. The team is continuing to study other traits to better understand how the first flower emerged. Explore further: What 'pine' cones reveal about the evolution of flowers More information: Edwige Moyroud et al. A link between LEAFY and B-gene homologues insheds light on ancestral mechanisms prefiguring floral development, New Phytologist (2017). DOI: 10.1111/nph.14483

Facchini A.,U. Warsaw | Venema Y.,U. Amsterdam | Zanasi F.,ENS Lyon
Proceedings - Symposium on Logic in Computer Science | Year: 2013

We provide a characterization theorem, in the style of van Ben them and Janin-Walukiewicz, for the alternation-free fragment of the modal mu-calculus. For this purpose we introduce a variant of standard monadic second-order logic (MSO), which we call well-founded monadic second-order logic (WFMSO). When interpreted in a tree model, the second-order quantifiers of WFMSO range over subsets of conversely well-founded sub trees. The first main result of the paper states that the expressive power of WFMSO over trees exactly corresponds to that of weak MSO-Automata. Using this automata-theoretic characterization, we then show that, over the class of all transition structures, the bisimulation-invariant fragment of WFMSO is the alternation-free fragment of the modal mu-calculus. As a corollary, we find that the logics WFMSO and WMSO (weak monadic second-order logic, where second-order quantification concerns finite subsets), are incomparable in expressive power. © 2013 IEEE.

Gueudre L.,French Institute of Petroleum | Jolimaite E.,French Institute of Petroleum | Bats N.,French Institute of Petroleum | Dong W.,ENS Lyon
Adsorption | Year: 2010

Gravimetric uptake measurements were performed with cyclohexane for different Silicalite-1 crystals sizes. It was observed that the apparent diffusion coefficients vary with crystal size, confirming the existence of a surface resistance. Considering that surface and the intracrystalline characteristic diffusion times are additives, it was possible to dissociate the two resistances. Surface mass transfer coefficient was found to be in the same order of magnitude for the different samples and activated with temperature. The contribution of surface resistance to mass transfer limitation is lower at high temperatures and for the bigger crystals. Surface resistance is far from being negligible for the smaller crystals: for crystals of 2 μm, surface resistance represents more than 60% of the total mass transfer resistance at 398 K. And crystals of that size (in the order of 2 μm) are usually used industrially, in order to minimize mass transfer resistance. The surface of one of our sample was purified by etching with a solution of hydrogen fluoride, without any enhancement of the adsorption kinetic. Surface resistance may not be located at the extreme surface of the crystals but in a layer of non negligible thickness of distorted crystal structure around the crystals. © 2010 Springer Science+Business Media, LLC.

Talon A.,ENS Lyon | Kratochvil J.,Charles University
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2015

We describe the missing class of the hierarchy of mixed unit interval graphs, generated by the intersection graphs of closed, open and one type of half-open intervals of the real line. This class lies strictly between unit interval graphs and mixed unit interval graphs. We give a complete characterization of this new class, as well as a polynomial time algorithm to recognize graphs from this class and to produce a corresponding interval representation if one exists. © IFIP International Federation for Information Processing 2015.

Krishnaswami N.R.,University of Birmingham | Pradic P.,ENS Lyon | Benton N.,Microsoft
Conference Record of the Annual ACM Symposium on Principles of Programming Languages | Year: 2015

In this paper, we show how to integrate linear types with type dependency, by extending the linear/non-linear calculus of Benton to support type dependency. Next, we give an application of this calculus by giving a proof-theoretic account of imperative programming, which requires extending the calculus with computationally irrelevant quantification, proof irrelevance, and a monad of computations. We show the soundness of our theory by giving a realizability model in the style of Nuprl, which permits us to validate not only the β-laws for each type, but also the η-laws. These extensions permit us to decompose Hoare triples into a collection of simpler type-theoretic connectives, yielding a rich equational theory for dependently-typed higherorder imperative programs. Furthermore, both the type theory and its model are relatively simple, even when all of the extensions are considered. Copyright © 2015 by the Association for Computing Machinery, Inc. (ACM).

Gregoire T.,ENS Lyon | Chlipala A.,Massachusetts Institute of Technology
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2016

The class of stencil programs involves repeatedly updating elements of arrays according to fixed patterns, referred to as stencils. Stencil problems are ubiquitous in scientific computing and are used as an ingredient to solve more involved problems. Their high regularity allows massive parallelization. Two important challenges in designing such algorithms are cache efficiency and minimizing the number of communication steps between nodes. In this paper, we introduce a mathematical framework for a crucial aspect of formal verification of both sequential and distributed stencil algorithms, and we describe its Coq implementation. We present a domain-specific embedded programming language with support for automating the most tedious steps of proofs that nested loops respect dependencies, applicable to sequential and distributed examples. Finally, we evaluate the robustness of our library by proving the dependency-correctness of some real-world stencil algorithms, including a state-of-the-art cache-oblivious sequential algorithm, as well as two optimized distributed kernels. © Springer International Publishing Switzerland 2016.

Crubille R.,ENS Lyon | Dal Lago U.,University of Bologna
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is applied to a typed, call-by-value, lambda-calculus. Surprisingly, the obtained relation coincides with context equivalence, contrary to what happens when call-by-name evaluation is considered. Even more surprisingly, full-abstraction only holds in a symmetric setting. © 2014 Springer-Verlag.

Crubille R.,ENS Lyon | Lago U.D.,French Institute for Research in Computer Science and Automation
Proceedings - Symposium on Logic in Computer Science | Year: 2015

Terms of Church's λ-calculus can be considered equivalent along many different definitions, but context equiv-alence is certainly the most direct and universally accepted one. If the underlying calculus becomes probabilistic, however, equivalence is too discriminating: terms which have totally unrelated behaviours are treated the same as terms which behave very similarly. We study the problem of evaluating the distance between affine λ-terms. A natural generalisation of context equiv-alence, is shown to be characterised by a notion of trace distance, and to be bounded from above by a co inductively defined distance based on the Kantorovich metric on distributions. A different, again fully-abstract, tuple-based notion of trace distance is shown to be able to handle nontrivial examples. © 2015 IEEE.

Keller C.,ENS Lyon | Keller C.,French Institute for Research in Computer Science and Automation | Werner B.,French Institute for Research in Computer Science and Automation
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

We present a new scheme to translate mathematical developments from HOL Light to Coq, where they can be re-used and re-checked. By relying on a carefully chosen embedding of Higher-Order Logic into Type Theory, we try to avoid some pitfalls of inter-operation between proof systems. In particular, our translation keeps the mathematical statements intelligible. This translation has been implemented and allows the importation of the HOL Light basic library into Coq. © 2010 Springer-Verlag.

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