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Theses

Du typage vectoriel

Abstract : The objective of this thesis is to develop a type theory for the linear-algebraic λ-calculus, an extension of λ-calculus motivated by quantum computing. This algebraic extension encompass all the terms of λ-calculus together with their linear combinations, so if t and r are two terms, so is α.t + β.r, with α and β being scalars from a given ring. The key idea and challenge of this thesis was to introduce a type system where the types, in the same way as the terms, form a vectorial space, providing the information about the structure of the normal form of the terms. This thesis presents the system Lineal, and also three intermediate systems, however interesting by themselves: Scalar, Additive and λCA, all of them with their subject reduction and strong normalisation proofs.
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Submitted on : Wednesday, October 12, 2011 - 3:38:22 PM
Last modification on : Friday, March 25, 2022 - 9:40:42 AM
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Alejandro Diaz Caro. Du typage vectoriel. Autre [cs.OH]. Université de Grenoble, 2011. Français. ⟨NNT : 2011GRENM038⟩. ⟨tel-00631514⟩

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