Realizability Interpretation and Normalization of Typed Call-by-Need λ\lambda-calculus With Control

We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need \lambda$-$calculus with control due to Ariola et al. Indeed, in such call-by-need calculus, substitutions have to be delayed until knowing if an argument is really needed. In a second step, we extend the proof to a call-by-need \lambda$$-calculus equipped with a type system equivalent to classical second-order predicate logic, representing one step towards proving the normalization of the call-by-need classical second-order arithmetic introduced by the second author to provide a proof-as-program interpretation of the axiom of dependent choice

Interactions of ribonucleotides with aluminium and iron oxides under varying environmental conditions

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Adsorption of ribonucleotides onto aluminum and iron oxides

International audienceMineral surfaces are known to adsorb organic molecules such as nucleic acids [1,2]. They might have concentrated the building blocks of biomolecules in the context of the origin of life, facilitating their polymerization. They also protect them from degradation [3,4] contributing to an extracellular genetic pool used by microorganisms in soils for horizontal gene transfers [5]. Previous work has highlighted the predominant role of the edges of mineral particles in the adsorption of nucleotides [6], implying oxide-like adsorption sites. Here we further investigate the interactions of ribonucleotides with alumina and hematite, as a function of pH, ionic strength and ligand-to-solid ratio. Batch adsorption experiments and surface complexation calculations using the Extended Triple Layer Model allow us to predict the speciation of the surface species, the stoichiometry and thermodynamic equilibrium constants for the adsorption of nucleotides. Both oxides lead to high values of adsorption of nucleotides (> 2 mol/m2). However, at high pH, hematite nanoparticles present a significantly higher adsorption compared to alumina. On alumina surfaces we propose the formation of a monodentate inner-sphere complex at low pH, and a bidentate outer-sphere complex at higher pH, both involving the negatively charged phosphate group [8]. This pH-dependency might have implications for the availability of nucleotides both in the context of the origin of life for polymerization and in modern soils for transfectio

Colloidal and chemical stabilities of iron oxide nanoparticles in aqueous solutions: the interplay of structural, chemical and environmental drivers

International audienceNanoparticle (NP) stability in aqueous environments is dependent upon many parameters including environmental conditions, NP concentrations as well as NP intrinsic characteristics. In this study, the effects of pH and surface modifications on the colloidal and chemical stabilities of nanosized magnetite (Fe3O4), maghemite (γ-Fe2O3) and hematite (α-Fe2O3) are investigated. Because changes in surface charge affect the size distribution of NP, pH plays a key role in driving the colloidal stability. More NP aggregation is observed at pH values close to the pH of zero point of charge (pHzpc). Coating of magnetite with humic acid (HA) and phosphatidylcholine (PC) affects the electrostatic interactions and then the colloidal behavior of NP. The rapid transformation of magnetite into maghemite through air oxidation results in significant modification of both surface charge and specific surface area of NP. Because the maghemite almost exclusively formed µm-scale aggregates, the colloidal stability of magnetite is expected to be hindered in oxic environments. For hematite, the particle size distribution data emphasize the influence of both pH and intrinsic surface properties in the colloidal stability. These findings may have strong implications for an accurate prediction of the transformation and mobility of Fe-nanoparticles under environmentally relevant conditions and thus their fate in nature

Realizability Interpretation and Normalization of Typed Call-by-Need λ-calculus With Control

International audienceWe define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need λ-calculus with control due to Ariola et al. Indeed, in such call-by-need calculus, substitutions have to be delayed until knowing if an argument is really needed. In a second step, we extend the proof to a call-by-need λ-calculus equipped with a type system equivalent to classical second-order predicate logic, representing one step towards proving the normalization of the call-by-need classical second-order arithmetic introduced by the second author to provide a proof-as-program interpretation of the axiom of dependent choice

Types by Need

International audienceA cornerstone of the theory of λ-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational models. Since the seminal work of de Carvalho in 2007, it is known that multi types (i.e. non-idempotent intersection types) refine intersection types with quantitative information and a strong connection to linear logic. Typically, type derivations provide bounds for evaluation lengths, and minimal type derivations provide exact bounds. De Carvalho studied call-by-name evaluation, and Kesner used his system to show the termination equivalence of call-by-need and call-by-name. De Carvalho's system, however, cannot provide exact bounds on call-by-need evaluation lengths. In this paper we develop a new multi type system for call-by-need. Our system produces exact bounds and induces a denotational model of call-by-need, providing the first tight quantitative semantics of call-by-need