Curry-style type Isomorphisms and Game Semantics

Curry-style system F, ie. system F with no explicit types in terms, can be seen as a core presentation of polymorphism from the point of view of programming languages. This paper gives a characterisation of type isomorphisms for this language, by using a game model whose intuitions come both from the syntax and from the game semantics universe. The model is composed of: an untyped part to interpret terms, a notion of game to interpret types, and a typed part to express the fact that an untyped strategy plays on a game. By analysing isomorphisms in the model, we prove that the equational system corresponding to type isomorphisms for Curry-style system F is the extension of the equational system for Church-style isomorphisms with a new, non-trivial equation: forall X.A = A[forall Y.Y/X] if X appears only positively in A.Comment: Accept\'e \`a Mathematical Structures for Computer Science, Special Issue on Type Isomorphism

Second-Order Type Isomorphisms Through Game Semantics

The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λ$\mu$-calculus, which can be seen as an extension of system F to classical logic, and for which we define a categorical framework: control hyperdoctrines. Our game model of λ$\mu$-calculus is based on polymorphic arenas (closely related to Hughes' hyperforests) which evolve during the play (following the ideas of Murawski-Ong). We show that type isomorphisms coincide with the "equality" on arenas associated with types. Finally we deduce the equational characterization of type isomorphisms from this equality. We also recover from the same model Roberto Di Cosmo's characterization of type isomorphisms for system F. This approach leads to a geometrical comprehension on the question of second order type isomorphisms, which can be easily extended to some other polymorphic calculi including additional programming features.Comment: accepted by Annals of Pure and Applied Logic, Special Issue on Game Semantic

Scale effects on the response of composite structures under impact loading

For several years, composite materials have taken a significant part in the realization of structures designed for transport (aeronautical, nautical, automotive. . .). In order to qualify the behavior of such structures, preliminary validation tests have to be done. These specific tests are often very expensive and difficult to set up, especially when the structure dimensions are large (fuselages of aircraft, ship hulls. . .). An alternative way is then to employ small-scale models. The use of these reduced scale structures requires the identification of similitude models allowing the extrapolation of the small-scale model behavior to the real structure. Although largely developed in the case of homogeneous materials, such similitude techniques are not clearly identified for composite materials taking into account the damage evolution during an impact. The purpose of this article is firstly to present existing similitude techniques making it possible to predict the composite structure behaviour from the knowledge of small-scale model response. Secondly, experiments were done on two scale of samples carried out by stratification of unidirectional carbon/epoxy plies. These results were finally compared with the analytical predictions of similitude laws currently used. The aim of this paper is to contribute to similitude laws development applied to composite structures. These laws permit to extrapolate the small-scale model behavior to the real scale one. Existing approaches have been established following two different methods. They are summarized in this paper and applied to impact loadings on two laminated plate scales. In order to complete data collected by ‘‘conventional’’ instrumentation (force transducer, displacement sensor, accelerometer.. .), optical device such as an high-velocity CCD camera, associated with optical techniques for the monitoring of markers, were used. These techniques make possible to compare displacement lines corresponding to each scale. It is shown that existing similitude laws, used for elastic materials, do not allow to simulate the behavior of the real scale when this one is damaged

L'importance de la coopération intercommunale

Después de años el gobierno se ha dado cuenta de la desorganización que hay en el litoral vasco. Aunque parece haber una cooperación transfronteriza, ésta parece no haber dado mucho resultad