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Preuves, Types et Sous-types

Abstract : This thesis is about the theoretical and practical study of a type system applied to functionnal programming certification. The base system is system ST invented by C.Raffalli; this system embeds polymorphism, subtyping and omission of non-algorithmic content. We firstly study models of this theory defined by the type system, building an axiomatic basis based on lattices that allows to express both calculus and logic. On this base, we study the type system itself, prove subject reduction, and the possibility of defining inside the system normalisability and reducibility properties. In the continuation, more applied, we study encoding of rich datatypes inspired from functionnal languages -including first-order modules- into Lambda-Calculus, and show that they behave well in the system through an embedding. The methodology of this part allows to extend the language preserving a consistency criterion ensuring the safety of the typed code.
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Contributor : Frédéric Ruyer <>
Submitted on : Wednesday, April 4, 2007 - 3:57:45 PM
Last modification on : Friday, November 6, 2020 - 3:28:44 AM
Long-term archiving on: : Thursday, April 8, 2010 - 2:53:46 PM



  • HAL Id : tel-00140046, version 1



Frédéric Ruyer. Preuves, Types et Sous-types. Mathématiques [math]. Université de Savoie, 2006. Français. ⟨tel-00140046⟩



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