Axiomatic Rewriting Theory I : A Diagrammatic Standardization Theorem
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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