Fundamentals of Compositional Rewriting Theory - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Logical and Algebraic Methods in Programming Année : 2023

Fundamentals of Compositional Rewriting Theory

Résumé

A foundational theory of compositional categorical rewriting theory is presented, based on a collection of fibration-like properties that collectively induce and structure intrinsically the large collection of lemmata used in the proofs of theorems such as concurrency and associativity. The resulting highly generic proofs of these theorems are given; it is noteworthy that the proof of the concurrency theorem takes only a few lines and, while that of associativity remains somewhat longer, it would be unreadably long if written directly in terms of the basic lemmata. In addition to improving, or even enabling, the readability of human-written proofs, we anticipate that this more generic and modular style of writing proofs should organize and inform the production of formalized proofs in a proof assistant such as Coq or Isabelle. A curated list of known instances of our framework is used to conclude the paper with a detailed discussion of the conditions under which the Double Pushout and Sesqui-Pushout semantics of graph transformation are compositional.
Fichier principal
Vignette du fichier
NBRHJK-ICGT-2021-extended (1).pdf (2.04 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03739405 , version 1 (10-10-2023)

Identifiants

Citer

Nicolas Behr, Russ Harmer, Jean Krivine. Fundamentals of Compositional Rewriting Theory. Journal of Logical and Algebraic Methods in Programming, 2023, 135, pp.100893. ⟨10.1016/j.jlamp.2023.100893⟩. ⟨hal-03739405⟩
66 Consultations
12 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More