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Ordered and Combinatorial Structures for Higher-Dimensional Rewriting
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0001-6140-180X
2016 (English)In: / [ed] Samuel Mimram, 2016Conference paper, Published paper (Refereed)
Abstract [en]

In principle, rewriting is the logically pure activity of transforming abstract expressions according to fully formalised rules, but in practice there is a significant interplay between abstract rules, more-or-less concrete interpretations, and a variety of book-keeping devices that all need to fit together if the rewriting process is to yield results. This paper presents elementary realisations of book-keeping and other formalising devices that are useful in higher-dimensional rewriting, with a focus on the "2-dimensional" case (PROPs and other types of monoidal category). In particular, it explains how one may construct a variety of ordering relations on these object that are sensitive to differences in the underlying graph structure of the objects being rewritten. It also shows how the formal feedback operation can be used to handle nonconvex redexes, which is a phenomenon of higher-dimensional rewriting that lacks a counterpart in word or term rewriting.

Place, publisher, year, edition, pages
2016.
Keyword [en]
rewriting, network rewriting, PROP, monoidal category, order relation, biaffine PROP, PROP with formal feedback
National Category
Algebra and Logic Discrete Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-33075OAI: oai:DiVA.org:mdh-33075DiVA: diva2:962976
Conference
Second edition of the workshop on Higher-Dimensional Rewriting and Applications 22-26 June 2016, Porto, Portugal http://hdra.gforge.inria.fr/ Co-located with the FSCD conference
Note

These proceedings were distributed (electronically on USB stick) to all participants at the FSCD conference and associated workshops.

Available from: 2016-09-07 Created: 2016-09-06 Last updated: 2016-12-12Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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  • asciidoc
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