A Reasonably Gradual Type Theory

Gradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized gradual type theory that admits three variants, each sacrificing one of these properties. For devising a gradual proof assistant based on CIC, normalization and conservativity with respect to CIC are key, but the tension with graduality needs to be addressed. Additionally, several challenges remain: (1) The presence of two wildcard terms at any type-the error and unknown terms-enables trivial proofs of any theorem, jeopardizing the use of a gradual type theory in a proof assistant; (2) Supporting general indexed inductive families, most prominently equality, is an open problem; (3) Theoretical accounts of gradual typing and graduality so far do not support handling type mismatches detected during reduction; (4) Precision and graduality are external notions not amenable to reasoning within a gradual type theory. All these issues manifest primally in CastCIC, the cast calculus used to define GCIC. In this work, we present an extension of CastCIC called GRIP. GRIP is a reasonably gradual type theory that addresses the issues above, featuring internal precision and general exception handling. GRIP features an impure (gradual) sort of types inhabited by errors and unknown terms, and a pure (non-gradual) sort of strict propositions for consistent reasoning about gradual terms. Internal precision supports reasoning about graduality within GRIP itself, for instance to characterize gradual exception-handling terms, and supports gradual subset types. We develop the metatheory of GRIP using a model formalized in Coq, and provide a prototype implementation of GRIP in Agda.Comment: 27pages + 2pages bibliograph

Conception du diplôme et formes d’usage du CAP

En s'appuyant sur le cas particulier du C.A.P. cet article est une réflexion plus générale sur la nature des diplômes professionnels. L'approche historique du processus de création, rénovation et suppression des C.A.P. témoigne du caractère évolutif d'un diplôme professionnel dans sa fonction première de préparation à l'accès à l'emploi. Elle met l'accent sur l'interdépendance des diplômes et sur les risques d'affaiblissement, le cas échéant, du rôle joué par chacun d'eux. Elle analyse l'offre actuelle de formation et de certification en C.A.P., ainsi que les ajustements opérés sur le marché du travail. Les auteurs concluent à une plus ou moins grande capacité du diplôme, selon les périodes, à concilier les logiques différentes qui président à la fois à sa conception et aux usages qui en sont faits par les systèmes éducatif et productif.Based on the particular case of the C.A.P. this article provides a more general reflection on the nature of professional diplomas. An historical approach to the process of creation, restoration and removal of the C.A.P. shows the evolutionary character of a professional diplorna in its primary function as a means of preparation to employnent access. It stresses the interdependence of diplomas and, in some cases, the risks of diminution of the rote played by each one of them. It studies the current offer in C.A.P. formation and certification, as well as the adjustments related to the labour market. The authors conclude that, depending on the time period, die diploma may be more or less successful in reconciling Me different objectives which govern its conception, and Us use by educational and production systems

A Reasonably Gradual Type Theory

International audienceGradualizing the Calculus of Inductive Constructions (CIC) involves dealing with subtle tensions between normalization, graduality, and conservativity with respect to CIC. Recently, GCIC has been proposed as a parametrized gradual type theory that admits three variants, each sacrificing one of these properties. For devising a gradual proof assistant based on CIC, normalization and conservativity with respect to CIC are key, but the tension with graduality needs to be addressed. Additionally, several challenges remain: (1) The presence of two wildcard terms at any type-the error and unknown terms-enables trivial proofs of any theorem, jeopardizing the use of a gradual type theory in a proof assistant; (2) Supporting general indexed inductive families, most prominently equality, is an open problem; (3) Theoretical accounts of gradual typing and graduality so far do not support handling type mismatches detected during reduction; (4) Precision and graduality are external notions not amenable to reasoning within a gradual type theory. All these issues manifest primally in CastCIC, the cast calculus used to define GCIC. In this work, we present an alternative to CastCIC called GRIP. GRIP is a reasonably gradual type theory that addresses the issues above, featuring internal precision and general exception handling. For consistent reasoning about gradual terms, GRIP features an impure sort of types inhabited by errors and unknown terms, and a pure sort of strict propositions. By adopting a novel interpretation of the unknown term that carefully accounts for universe levels, GRIP satisfies graduality for a large and well-defined class of terms, in addition to being normalizing and a conservative extension of CIC. Internal precision supports reasoning about graduality within GRIP itself, for instance to characterize gradual exception-handling terms, and supports gradual subset types. We develop the metatheory of GRIP using a model formalized in Coq, and provide a prototype implementation of GRIP in Agda

The Multiverse: Logical Modularity for Proof Assistants

Proof assistants play a dual role as programming languages and logical systems. As programming languages, proof assistants offer standard modularity mechanisms such as first-class functions, type polymorphism and modules. As logical systems, however, modularity is lacking, and understandably so: incompatible reasoning principles-such as univalence and uniqueness of identity proofs-can indirectly lead to logical inconsistency when used in a given development, even when they appear to be confined to different modules. The lack of logical modularity in proof assistants also hinders the adoption of richer programming constructs, such as effects. We propose the multiverse, a general type-theoretic approach to endow proof assistants with logical modularity. The multiverse consists of multiple universe hierarchies that statically describe the reasoning principles and effects available to define a term at a given type. We identify sufficient conditions for this structuring to modularly ensure that incompatible principles do not interfere, and to locally restrict the power of dependent elimination when necessary. This extensible approach generalizes the ad-hoc treatment of the sort of propositions in the Coq proof assistant. We illustrate the power of the multiverse by describing the inclusion of Coq-style propositions, the strict propositions of Gilbert et al., the exceptional type theory of Pédrot and Tabareau, and general axiomatic extensions of the logic

The Multiverse: Logical Modularity for Proof Assistants

Proof assistants play a dual role as programming languages and logical systems. As programming languages, proof assistants offer standard modularity mechanisms such as first-class functions, type polymorphism and modules. As logical systems, however, modularity is lacking, and understandably so: incompatible reasoning principles-such as univalence and uniqueness of identity proofs-can indirectly lead to logical inconsistency when used in a given development, even when they appear to be confined to different modules. The lack of logical modularity in proof assistants also hinders the adoption of richer programming constructs, such as effects. We propose the multiverse, a general type-theoretic approach to endow proof assistants with logical modularity. The multiverse consists of multiple universe hierarchies that statically describe the reasoning principles and effects available to define a term at a given type. We identify sufficient conditions for this structuring to modularly ensure that incompatible principles do not interfere, and to locally restrict the power of dependent elimination when necessary. This extensible approach generalizes the ad-hoc treatment of the sort of propositions in the Coq proof assistant. We illustrate the power of the multiverse by describing the inclusion of Coq-style propositions, the strict propositions of Gilbert et al., the exceptional type theory of Pédrot and Tabareau, and general axiomatic extensions of the logic

Dijkstra monads for all

This paper proposes a general semantic framework for verifying programs with arbitrary monadic side-effects using Dijkstra monads, which we define as monad-like structures indexed by a specification monad. We prove that any monad morphism between a computational monad and a specification monad gives rise to a Dijkstra monad, which provides great flexibility for obtaining Dijkstra monads tailored to the verification task at hand. We moreover show that a large variety of specification monads can be obtained by applying monad transformers to various base specification monads, including predicate transformers and Hoare-style pre- and postconditions. For defining correct monad transformers, we propose a language inspired by Moggi's monadic metalanguage that is parameterized by a dependent type theory. We also develop a notion of algebraic operations for Dijkstra monads, and start to investigate two ways of also accommodating effect handlers. We implement our framework in both Coq and F*, and illustrate that it supports a wide variety of verification styles for effects such as exceptions, nondeterminism, state, input-output, and general recursion

Hepatitis C Virus Core Protein Induces Neuroimmune Activation and Potentiates Human Immunodeficiency Virus-1 Neurotoxicity

BACKGROUND: Hepatitis C virus (HCV) genomes and proteins are present in human brain tissues although the impact of HIV/HCV co-infection on neuropathogenesis remains unclear. Herein, we investigate HCV infectivity and effects on neuronal survival and neuroinflammation in conjunction with HIV infection. METHODOLOGY: Human microglia, astrocyte and neuron cultures were infected with cell culture-derived HCV or exposed to HCV core protein with or without HIV-1 infection or HIV-1 Viral Protein R (Vpr) exposure. Host immune gene expression and cell viability were measured. Patch-clamp studies of human neurons were performed in the presence or absence of HCV core protein. Neurobehavioral performance and neuropathology were examined in HIV-1 Vpr-transgenic mice in which stereotaxic intrastriatal implants of HCV core protein were performed. PRINCIPAL FINDINGS: HCV-encoded RNA as well as HCV core and non-structural 3 (NS3) proteins were detectable in human microglia and astrocytes infected with HCV. HCV core protein exposure induced expression of pro-inflammatory cytokines including interleukin-1β, interleukin-6 and tumor necrosis factor-α in microglia (p<0.05) but not in astrocytes while increased chemokine (e.g. CXCL10 and interleukin-8) expression was observed in both microglia and astrocytes (p<0.05). HCV core protein modulated neuronal membrane currents and reduced both β-III-tubulin and lipidated LC3-II expression (p<0.05). Neurons exposed to supernatants from HCV core-activated microglia exhibited reduced β-III-tubulin expression (p<0.05). HCV core protein neurotoxicity and interleukin-6 induction were potentiated by HIV-1 Vpr protein (p<0.05). HIV-1 Vpr transgenic mice implanted with HCV core protein showed gliosis, reduced neuronal counts together with diminished LC3 immunoreactivity. HCV core-implanted animals displayed neurobehavioral deficits at days 7 and 14 post-implantation (p<0.05). CONCLUSIONS: HCV core protein exposure caused neuronal injury through suppression of neuronal autophagy in addition to neuroimmune activation. The additive neurotoxic effects of HCV- and HIV-encoded proteins highlight extrahepatic mechanisms by which HCV infection worsens the disease course of HIV infection

Bone marrow graft versus peripheral blood graft in haploidentical hematopoietic stem cells transplantation: a retrospective analysis in1344 patients of SFGM-TC registry.

peer reviewedThe use of peripheral blood (PB) or bone marrow (BM) stem cells graft in haploidentical hematopoietic stem cell transplantation with post-transplant cyclophosphamide (PTCy) for graft-versus-host disease (GVHD) prophylaxis remains controversial. Moreover, the value of adding anti-thymoglobulin (ATG) to PTCy is unknown. A total of 1344 adult patients received an unmanipulated haploidentical transplant at 37 centers from 2012 to 2019 for hematologic malignancy. We compared the outcomes of patients according to the type of graft, using a propensity score analysis. In total population, grade II-IV and III-IV acute GVHD (aGVHD) were lower with BM than with PB. Grade III-IV aGVHD was lower with BM than with PB + ATG. All outcomes were similar in PB and PB + ATG groups. Then, in total population, adding ATG does not benefit the procedure. In acute leukemia, myelodysplastic syndrome and myeloproliferative syndrome (AL-MDS-MPS) subgroup receiving non-myeloablative conditioning, risk of relapse was twice greater with BM than with PB (51 vs. 22%, respectively). Conversely, risk of aGVHD was greater with PB (38% for aGVHD II-IV; 16% for aGVHD III-IV) than with BM (28% for aGVHD II-IV; 8% for aGVHD III-IV). In this subgroup with intensified conditioning regimen, risk of relapse became similar with PB and BM but risk of aGVHD III-IV remained higher with PB than with BM graft (HR = 2.0; range [1.17-3.43], p = 0.012)

Chanson française : un étayage à la compréhension de texte et à l'acquisition de vocabulaire ? Un levier de différenciation pédagogique ? Étude-terrain/recherche-action auprès d'élèves de cycle 3

The issues of reading comprehension for schooling and for the future life of students are known and taken into account by all actors in the educational community and national education policies. This work is a proposal to take into account differencies between students in order to improve their reading, oral and vocabulary acquisition skills by using an alternative reading device : listening to a song with narrative text. The results are encouraging in improving the undestanding of a text, especially on the implicit level of the text, but are less convincing for the increase of vocabulary learning. The results show that the listening of a song seems to represent a support for the students presenting the most sifficulties in comprehension of writing field's.Les enjeux de la lecture compréhension pour la scolarité et pour la vie future des élèves sont connus et pris en compte par l'ensemble des acteurs de la communauté éducative et les politiques mises en œuvre par le Ministère de l'Éducation Nationale. Ce travail est une proposition de prise en compte des différences entre les élèves afin d'améliorer leurs compétences de compréhension de l'écrit, de l'oral et l'acquisition de mots de vocabulaire, en utilisant un dispositif alternatif à la lecture : l'écoute d'une chanson à texte narratif. Les résultats sont encourageants en ce qui concerne l'amélioration de la compréhension d'un texte, notamment sur le niveau implicite du texte, mais se révèlent moins probants pour l'augmentation de l'apprentissage du vocabulaire. Les résultats montrent que l'écoute d'une chanson semble représenter un étayage pour les élèves présentant le plus de difficultés dans le domaine de la compréhension de l'écrit