Relational type-checking for MELL proof-structures. Part 1: Multiplicatives

Relational semantics for linear logic is a form of non-idempotent intersection type system, from which several informations on the execution of a proof-structure can be recovered. An element of the relational interpretation of a proof-structure R with conclusion $\Gamma$ acts thus as a type (refining $\Gamma$) having R as an inhabitant. We are interested in the following type-checking question: given a proof-structure R, a list of formulae $\Gamma$, and a point x in the relational interpretation of $\Gamma$, is x in the interpretation of R? This question is decidable. We present here an algorithm that decides it in time linear in the size of R, if R is a proof-structure in the multiplicative fragment of linear logic. This algorithm can be extended to larger fragments of multiplicative-exponential linear logic containing $\lambda$-calculus

Glueability of Resource Proof-Structures: Inverting the Taylor Expansion

A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are part of the Taylor expansion of some MELL proof-structure, through a rewriting system acting both on resource and MELL proof-structures

A Functorial Bridge between the Infinitary Affine Lambda-Calculus and Linear Logic

International audienceIt is a well known intuition that the exponential modality of linear logic may be seen as a form of limit. Recently,Mellì es, Tabareau and Tasson gave a categorical account for this intuition, whereas the first author provided a topological account, based on an infinitary syntax. We relate these two different views by giving a categorical version of the topological construction, yielding two benefits: on the one hand, we obtain canonical models of the infinitary affine lambda-calculus introduced by the first author; on the other hand, we find an alternative formula for computing free commutative comonoids in models of linear logic with respect to the one presented byMellì es et al

Injectivity of relational semantics for (connected) MELL proof-nets via Taylor expansion

International audienceWe show that: (1) the Taylor expansion of a cut-free MELL proof-structure R with atomic axioms is the (most informative part of the) relational semantics of R; (2) every (connected) MELL proof-net is uniquely determined by the element of order 2 of its Taylor expansion; (3) the relational semantics is injective for (connected) MELL proof-nets

Gluing resource proof-structures: inhabitation and inverting the Taylor expansion

A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are part of the Taylor expansion of some MELL proof-structure, through a rewriting system acting both on resource and MELL proof-structures. As a consequence, we also prove semi-decidability of the type inhabitation problem for cut-free MELL proof-structures.Comment: arXiv admin note: substantial text overlap with arXiv:1910.0793

33èmes Journées Francophones des Langages Applicatifs

International audienceLes 33èmes Journées Francophones des Langages Applicatifs (JFLA) se sont tenues à Saint-Médard-d'Excideuil, plus précisément Domaine d'Essendiéras (Périgord), du mardi 28 juin 2022 au vendredi 1er juillet 2022.Les JFLA réunissent concepteurs, utilisateurs et théoriciens ; elles ont pour ambition de couvrir les domaines des langages applicatifs, de la preuve formelle, de la vérification de programmes, et des objets mathématiques qui sous-tendent ces outils. Ces domaines doivent être pris au sens large : nous souhaitons promouvoir les ponts entre les différentes thématiques.- Langages fonctionnels et applicatifs : sémantique, compilation, optimisation, typage, mesures, extensions par d'autres paradigmes.- Assistants de preuve : implémentation, nouvelles tactiques, développements présentant un intérêt technique ou méthodologique.- Logique, correspondance de Curry-Howard, réalisabilité, extraction de programmes, modèles.- Spécification, prototypage, développements formels d'algorithmes.- Vérification de programmes ou de modèles, méthode déductive, interprétation abstraite, raffinement.- Utilisation industrielle des langages fonctionnels et applicatifs, ou des méthodes issues des preuves formelles, outils pour le web.Les articles soumis aux JFLA sont relus par au moins deux personnes s'ils sont acceptés, trois personnes s'ils sont rejetés. Les critiques des relecteurs sont toujours bienveillantes et la plupart du temps encourageantes et constructives, même en cas de rejet

Leaf metabolic traits reveal hidden dimensions of plant form and function

International audienceThe metabolome is the biochemical basis of plant form and function, but we know little about its macroecological variation across the plant kingdom. Here, we used the plant functional trait concept to interpret leaf metabolome variation among 457 tropical and 339 temperate plant species. Distilling metabolite chemistry into five metabolic functional traits reveals that plants vary on two major axes of leaf metabolic specialization—a leaf chemical defense spectrum and an expression of leaf longevity. Axes are similar for tropical and temperate species, with many trait combinations being viable. However, metabolic traits vary orthogonally to life-history strategies described by widely used functional traits. The metabolome thus expands the functional trait concept by providing additional axes of metabolic specialization for examining plant form and function

Leaf metabolic traits reveal hidden dimensions of plant form and function

The metabolome is the biochemical basis of plant form and function, but we know little about its macroecological variation across the plant kingdom. Here, we used the plant functional trait concept to interpret leaf metabolome variation among 457 tropical and 339 temperate plant species. Distilling metabolite chemistry into five metabolic functional traits reveals that plants vary on two major axes of leaf metabolic specialization—a leaf chemical defense spectrum and an expression of leaf longevity. Axes are similar for tropical and temperate species, with many trait combinations being viable. However, metabolic traits vary orthogonally to life-history strategies described by widely used functional traits. The metabolome thus expands the functional trait concept by providing additional axes of metabolic specialization for examining plant form and function

The ANTENATAL multicentre study to predict postnatal renal outcome in fetuses with posterior urethral valves: objectives and design

Abstract Background Posterior urethral valves (PUV) account for 17% of paediatric end-stage renal disease. A major issue in the management of PUV is prenatal prediction of postnatal renal function. Fetal ultrasound and fetal urine biochemistry are currently employed for this prediction, but clearly lack precision. We previously developed a fetal urine peptide signature that predicted in utero with high precision postnatal renal function in fetuses with PUV. We describe here the objectives and design of the prospective international multicentre ANTENATAL (multicentre validation of a fetal urine peptidome-based classifier to predict postnatal renal function in posterior urethral valves) study, set up to validate this fetal urine peptide signature. Methods Participants will be PUV pregnancies enrolled from 2017 to 2021 and followed up until 2023 in >30 European centres endorsed and supported by European reference networks for rare urological disorders (ERN eUROGEN) and rare kidney diseases (ERN ERKNet). The endpoint will be renal/patient survival at 2 years postnatally. Assuming α = 0.05, 1–β = 0.8 and a mean prevalence of severe renal outcome in PUV individuals of 0.35, 400 patients need to be enrolled to validate the previously reported sensitivity and specificity of the peptide signature. Results In this largest multicentre study of antenatally detected PUV, we anticipate bringing a novel tool to the clinic. Based on urinary peptides and potentially amended in the future with additional omics traits, this tool will be able to precisely quantify postnatal renal survival in PUV pregnancies. The main limitation of the employed approach is the need for specialized equipment. Conclusions Accurate risk assessment in the prenatal period should strongly improve the management of fetuses with PUV