Skip to Main content Skip to Navigation
Theses

Structures et modèles de calculs de réécriture

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.
Document type :
Theses
Complete list of metadata

Cited literature [50 references]  Display  Hide  Download

https://hal.univ-lorraine.fr/tel-01748148
Contributor : Thèses Ul <>
Submitted on : Thursday, March 29, 2018 - 11:26:34 AM
Last modification on : Tuesday, May 29, 2018 - 3:22:56 PM
Long-term archiving on: : Thursday, September 13, 2018 - 11:47:40 PM

File

SCD_T_2007_0032_FAURE.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-01748148, version 1

Citation

Germain Faure. Structures et modèles de calculs de réécriture. Autre [cs.OH]. Université Henri Poincaré - Nancy 1, 2007. Français. ⟨NNT : 2007NAN10032⟩. ⟨tel-01748148v1⟩

Share

Metrics

Record views

23

Files downloads

6