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This paper presents a type theory in which it is possible to directly manipulate n-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways to reason about identity types, for instance, function extensionality is directly provable in the system. Further,(More)
This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive , and relies on nothing but the axioms and rules of the founda-tional framework implemented by Coq. To support the formalization, we developed a(More)
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties. The theory of real algebraic numbers and more generally of semi-algebraic varieties is at the core of a number(More)
Merci beaucoup à Lydie puis à Valérie ainsi qu'à Martine pour avoir toujours su m'accueillir avec le sourire, malgré tout ce que j'ai eu à vous demander, et pour avoir réglé tous mes problèmes avec une efficacité remarquable. Je n'en serais pas là sans ceux dont les enseignements ont marqué ma vie. Merci à Nicolas Tosel, pour m'avoir initié à l'algèbre.(More)
Human T lymphocyte virus type I (HTLV-I)-associated chronic inflammatory neurological disease (HTLV-I-associated myelopathy/tropical spastic paraparesis [HAM/TSP]) is suggested to be an immunopathologically mediated disorder characterized by large numbers of HTLV-I Tax-specific CD8+ T cells. The frequency of these cells in the peripheral blood and(More)
The recent characterization of MHC-displayed tumor-associated antigensthat recognize effector cells of the immune system has created new perspectives for cancer therapy. Antibodies that recognize these tumor-associated MHC-peptide complexes with the same specificity as the T-cell antigen receptor will therefore be valuable tools for immunotherapy as well as(More)
This paper shows a construction in Coq of the set of real algebraic numbers, together with a formal proof that this set has a structure of discrete Archimedean real closed field. This construction hence implements an interface of real closed field. Instances of such an interface immediately enjoy quantifier elimination thanks to a previous work. This work(More)
The advent in recent years of the application of tetrameric arrays of class I peptide-MHC complexes now enables us to detect and study rare populations of Ag-specific CD8(+) T cells. However, available methods cannot visualize or determine the number and distribution of these TCR ligands on individual cells nor detect APCs in tissues. In this study, we(More)