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Structures et modèles de calculs de réécriture

Germain Faure 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The rewriting calculus, also called the rho-calculus, is a generalisation of the lambda-calculus with matching capabilities and term aggregation. The abstraction on variables is replaced by the abstraction on patterns and the corresponding matching theory can be a priori arbitrary. The term aggregation is used to collect all possible results.
This thesis is devoted to the study of different combinations of the fundamental ingredients of the rho-calculus: matching, term aggregation and higher-order mechanisms.
We study higher-order matching in the pure lambda-calculus modulo a restriction of beta-conversion known as superdevelopments. This new approach is powerful enough to deal with second-order and higher-order Miller pattern-matching problems.
We next propose a categorical semantics for the parallel lambda-calculus that is nothing but an extension of the lambda-calculus with term aggregation. We show that it is a significant step towards a denotational semantics of the rewriting calculus.
We also study and compare pattern-based calculi where patterns can be dynamic in the sense that they can be instantiated and reduced. We show that this study, and particularly the confluence proof, is general enough so that it can be instantiated to recover all the already existing pattern-based calculi. We then study implementation of such calculi by proposing a rewriting calculus with explicit matching and explicit substitution application.
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Submitted on : Friday, July 20, 2007 - 6:27:17 PM
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Germain Faure. Structures et modèles de calculs de réécriture. Génie logiciel [cs.SE]. Université Henri Poincaré - Nancy 1, 2007. Français. ⟨NNT : 2007NAN10032⟩. ⟨tel-01748148v2⟩

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