Skip to Main content Skip to Navigation

Représentation d’algèbres non libres en théorie des types

Abstract : This thesis has two parts: one is the presentation of an extension of the calculus of inductive constructions($\mathcal{CIC}$) of Christine Paulin and Thierry Coquand, allowing the definition of non free types, the second is the development of a formal proof, in the proof assistant \coq, of self-stabilization of an distributed algorithm. The first theme is developed in part II and the second in part III, the part I is a general presentation of $\mathcal{CIC}$, which is the central subject of this work since it is also the underlying formalism of \coq. Our extension of $\mathcal{CIC}$ is mainly based on a new notion: \emph{normalized types}. A normalized type is built with a type $A$ and a function \nf\ on this type. Intuitively the normalized, noted $\norm(A,\nf)$ represents the quotient of type $A$ by the relation $R_\nf$ defined by $(R_\nf \ x\ y) \Leftrightarrow (\nf\ x)=(\nf\ y)$. We show that this equality can be included in the conversion without losing properties of $\mathcal{CIC}$: logical consistency, decidability of type checking etc.
Document type :
Complete list of metadata

Cited literature [268 references]  Display  Hide  Download
Contributor : Pierre Courtieu <>
Submitted on : Friday, January 31, 2020 - 2:01:14 PM
Last modification on : Wednesday, September 16, 2020 - 5:01:32 PM
Long-term archiving on: : Friday, May 1, 2020 - 12:12:20 PM


Files produced by the author(s)


  • HAL Id : tel-02346101, version 1



Pierre Courtieu. Représentation d’algèbres non libres en théorie des types. Logique en informatique [cs.LO]. Université Paris 11, 2001. Français. ⟨tel-02346101⟩



Record views


Files downloads