Building Decision Procedures in the Calculus of Inductive Constructions

It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent proposition P' obtained from P thanks to possibly complex calculations. In this paper, we investigate a new version of the calculus of inductive constructions which incorporates arbitrary decision procedures into deduction via the conversion rule of the calculus. The novelty of the problem in the context of the calculus of inductive constructions lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved

Certification of SAT Solvers in Coq

International audienceWe describe a fully portable, open source certifier for traces of SAT problems produced by zChaff. It can also be easily adapted for MiniSat, PicoSat or BooleForce, and we have done it for PicoSat. Our certifier has been developed with the proof assistant Coq. We give some figures based on the pigeon hole, comparing both PicoSat and zChaff on the one hand, and our certifier with another certifier also developed with Coq

From formal proofs to mathematical proofs: a safe, incremental way for building in first-order decision procedures

We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order decision procedures: deduction is still in charge of the CIC kernel, while computation is outsourced to dedicated first-order decision procedures that can be taken from the shelves provided they deliver a proof certificate. The soundness of the whole system becomes an incremental property following from the soundness of the certificate checkers and that of the kernel. A detailed example shows that the resulting style of proofs becomes closer to that of the working mathematician

HoME: a Household Multimodal Environment

We introduce HoME: a Household Multimodal Environment for artificial agents to learn from vision, audio, semantics, physics, and interaction with objects and other agents, all within a realistic context. HoME integrates over 45,000 diverse 3D house layouts based on the SUNCG dataset, a scale which may facilitate learning, generalization, and transfer. HoME is an open-source, OpenAI Gym-compatible platform extensible to tasks in reinforcement learning, language grounding, sound-based navigation, robotics, multi-agent learning, and more. We hope HoME better enables artificial agents to learn as humans do: in an interactive, multimodal, and richly contextualized setting.Comment: Presented at NIPS 2017's Visually-Grounded Interaction and Language Worksho

CoqMTU: a higher-order type theory with a predicative hierarchy of universes parametrized by a decidable first-order theory

International audienceWe study a complex type theory, a Calculus of Inductive Constructions with a predicative hierarchy of universes and a first-order theory T built in its conversion relation. The theory T is specified abstractly, by a set of constructors, a set of defined symbols, axioms expressing that constructors are free and defined symbols completely defined, and a generic elimination principle relying on crucial properties of first-order structures satisfying the axioms. We first show that CoqMTU enjoys all basic meta-theoretical properties of such calculi, confluence, subject reduction and strong normalization when restricted to weak-elimination, implying the decidability of type-checking in this case as well as consistency. The case of strong elimination is left open

Expression, purification, crystallization and preliminary X-ray analysis of the cathelicidin motif of the protegrin-3 precursor

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Coq without Type Casts: A Complete Proof of Coq Modulo Theory

International audienceIncorporating extensional equality into a dependent intensional type system such as the Calculus of Constructions provides with stronger type-checking capabilities and makes the proof development closer to intuition. Since strong forms of extensionality lead to undecidable type-checking, a good trade-off is to extend intensional equality with a decidable first-order theory T, as done in CoqMT, which uses matching modulo T for the weak and strong elimination rules, we call these rules T-elimination. So far, type-checking in CoqMT is known to be decidable in presence of a cumulative hierarchy of universes and weak T-elimination. Further, it has been shown by Wang with a formal proof in Coq that consistency is preserved in presence of weak and strong elimination rules, which actually implies consistency in presence of weak and strong T-elimination rules since T is already present in the conversion rule of the calculus. We justify here CoqMT's type-checking algorithm by showing strong normalization as well as the Church-Rosser property of β-reductions augmented with CoqMT's weak and strong T-elimination rules. This therefore concludes successfully the meta-theoretical study of CoqMT

Analysis of cellular responses of macrophages to zinc ions and zinc oxide nanoparticles: a combined targeted and proteomic approach

Two different zinc oxide nanoparticles, as well as zinc ions, are used to study the cellular responses of the RAW 264 macrophage cell line. A proteomic screen is used to provide a wide view of the molecular effects of zinc, and the most prominent results are cross-validated by targeted studies. Furthermore, the alteration of important macrophage functions (e.g. phagocytosis) by zinc is also investigated. The intracellular dissolution/uptake of zinc is also studied to further characterize zinc toxicity. Zinc oxide nanoparticles dissolve readily in the cells, leading to high intracellular zinc concentrations, mostly as protein-bound zinc. The proteomic screen reveals a rather weak response in the oxidative stress response pathway, but a strong response both in the central metabolism and in the proteasomal protein degradation pathway. Targeted experiments confirm that carbohydrate catabolism and proteasome are critical determinants of sensitivity to zinc, which also induces DNA damage. Conversely, glutathione levels and phagocytosis appear unaffected at moderately toxic zinc concentrations

Molecular responses of mouse macrophages to copper and copper oxide nanoparticles inferred from proteomic analyses

The molecular responses of macrophages to copper-based nanoparticles have been investigated via a combination of proteomic and biochemical approaches, using the RAW264.7 cell line as a model. Both metallic copper and copper oxide nanoparticles have been tested, with copper ion and zirconium oxide nanoparticles used as controls. Proteomic analysis highlighted changes in proteins implicated in oxidative stress responses (superoxide dismutases and peroxiredoxins), glutathione biosynthesis, the actomyosin cytoskeleton, and mitochondrial proteins (especially oxidative phosphorylation complex subunits). Validation studies employing functional analyses showed that the increases in glutathione biosynthesis and in mitochondrial complexes observed in the proteomic screen were critical to cell survival upon stress with copper-based nanoparticles; pharmacological inhibition of these two pathways enhanced cell vulnerability to copper-based nanoparticles, but not to copper ions. Furthermore, functional analyses using primary macrophages derived from bone marrow showed a decrease in reduced glutathione levels, a decrease in the mitochondrial transmembrane potential, and inhibition of phagocytosis and of lipopolysaccharide-induced nitric oxide production. However, only a fraction of these effects could be obtained with copper ions. In conclusion, this study showed that macrophage functions are significantly altered by copper-based nanoparticles. Also highlighted are the cellular pathways modulated by cells for survival and the exemplified cross-toxicities that can occur between copper-based nanoparticles and pharmacological agents

The drug and vaccine landscape for neglected diseases (2000–11): a systematic assessment

Background In 1975–99, only 1·1% of new therapeutic products had been developed for neglected diseases. Since then, several public and private initiatives have attempted to mitigate this imbalance. We analysed the research and development pipeline of drugs and vaccines for neglected diseases from 2000 to 2011. Methods We searched databases of drug regulatory authorities, WHO, and clinical trial registries for entries made between Jan 1, 2000, and Dec 31, 2011. We defi ned neglected diseases as malaria, tuberculosis, diarrhoeal diseases, neglected tropical diseases (NTDs; WHO defi nition), and other diseases of poverty according to common defi nitions. Findings Of the 850 new therapeutic products registered in 2000–11, 37 (4%) were indicated for neglected diseases, comprising 25 products with a new indication or formulation and eight vaccines or biological products. Only four new chemical entities were approved for neglected diseases (three for malaria, one for diarrhoeal disease), accounting for 1% of the 336 new chemical entities approved during the study period. Of 148 445 clinical trials registered in Dec 31, 2011, only 2016 (1%) were for neglected diseases. Interpretation Our fi ndings show a persistent insuffi ciency in drug and vaccine development for neglected diseases. Nevertheless, these and other data show a slight improvement during the past 12 years in new therapeutics development and registration. However, for many neglected diseases, new therapeutic products urgently need to be developed and delivered to improve control and potentially achieve elimination