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Chapitre D'ouvrage Année : 2005

Axiomatic Rewriting Theory I : A Diagrammatic Standardization Theorem

Paul-André Melliès

Résumé

By extending nondeterministic transition systems with concurrency and copy mechanisms, Axiomatic Rewriting Theory provides a uniform framework for a variety of rewriting systems, ranging from higher-order systems to Petri nets and process calculi. Despite its generality, the theory is surprisingly simple, based on a mild extension of transition systems with independence: an axiomatic rewriting system is defined as a 1-dimensional transition graph G equipped with 2-dimensional transitions describing the redex permutations of the system, and their orientation. In this article, we formulate a series of elementary axioms on axiomatic rewriting systems, and establish a diagrammatic standardization theorem.
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Dates et versions

hal-00151276 , version 1 (03-06-2007)

Identifiants

  • HAL Id : hal-00151276 , version 1

Citer

Paul-André Melliès. Axiomatic Rewriting Theory I : A Diagrammatic Standardization Theorem. Aart Middeldorp and Vincent van Oostrom and Femke van Raamsdonk and Roel C. de Vrijer. Processes, Terms and Cycles: Steps on the Road to Infinity, Essays Dedicated to Jan Willem Klop, on the Occasion of His 60th Birthday., Springer Verlag, pp.554-638, 2005. ⟨hal-00151276⟩
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