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Type systems and deduction in the rewriting calculus

Identifieur interne : 005B26 ( Main/Merge ); précédent : 005B25; suivant : 005B27

Type systems and deduction in the rewriting calculus

Auteurs : Benjamin Wack [France]

Source :

RBID : Hal:tel-00010546

Descripteurs français

mix :
- Lambda-calcul, déduction, filtrage, principe de Poincaré, réécriture, typage.

English descriptors

mix :
- Lambda-calculus, Poincaré principle, pattern matching, rewriting, type systems.

Abstract

The rewriting calculus is a lambda-calculus with pattern matching. This thesis is devoted to the study of type systems for this calculus, and to its applications to the domain of deduction.

We study two typing paradigms. The first one is inspired by the simply typed lambda-calculus, but it differs from it in the sense that a term may be well-typed without being terminating. Thus, we use it for representing programs and rewriting systems.

The second family of type systems we study is adapted from the Pure Type Systems. We show its strong normalization via a translation into a typed lambda-calculus.

Finally, we propose two ways of using the rewriting calculus in logic. In the first approach, we use the strongly normalizing systems to define proof terms for deduction modulo. In the second case, we define a generalization of natural deduction and we show that matching is useful in order to represent the rules of this deduction system.

Url:

https://tel.archives-ouvertes.fr/tel-00010546

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Le document en format XML

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The second family of type systems we study is adapted from the Pure Type Systems. We show its strong normalization via a translation into a typed lambda-calculus.

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Type systems and deduction in the rewriting calculus

Type systems and deduction in the rewriting calculus

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

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