License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2021.24
URN: urn:nbn:de:0030-drops-142620
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van Oostrom, Vincent

Z; Syntax-Free Developments

LIPIcs-FSCD-2021-24.pdf (0.9 MB)


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.

BibTeX - Entry

  author =	{van Oostrom, Vincent},
  title =	{{Z; Syntax-Free Developments}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{24:1--24:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-142620},
  doi =		{10.4230/LIPIcs.FSCD.2021.24},
  annote =	{Keywords: rewrite system, confluence, normalisation, recurrence}

Keywords: rewrite system, confluence, normalisation, recurrence
Collection: 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)
Issue Date: 2021
Date of publication: 06.07.2021

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