Semantic Apparatus – Z; Syntax-Free Developments

Cited by Lee Sonogan

Properties of the z-transform | Download Table

Abstract by van Oostrom, Vincent

We present the Z-property and instantiate it to various rewrite systems: associativity, positive braids, self-distributivity, the lambda-calculus, lambda-calculi with explicit substitutions, orthogonal TRSs, …. The Z-property is proven equivalent to Takahashi’s angle property by means of a syntax-free notion of development. We show that several classical consequences of having developments such as confluence, normalisation, and recurrence, can be regained in a syntax-free way, and investigate how the notion corresponds to the classical syntactic notion of development in term rewriting.

Publication: Universität Innsbruck, Austria (Peer-Reviewed Journal)

Pub Date: 6/7/2021 Doi: 10.4230/LIPIcs.FSCD.2021.24

Keywords: rewrite system, confluence, normalisation, recurrence (Plenty more sections and references in this research article)

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