License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2021.6
URN: urn:nbn:de:0030-drops-134407
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13440/
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Accattoli, Beniamino ; Faggian, Claudia ; Guerrieri, Giulio

Factorize Factorization

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LIPIcs-CSL-2021-6.pdf (0.7 MB)

Abstract

We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which is inspired by the Hindley-Rosen technique for confluence. Specifically, our approach is well adapted to deal with extensions of the call-by-name and call-by-value λ-calculi.
The technique is first developed abstractly. We isolate a sufficient condition (called linear swap) for lifting factorization from components to the compound system, and which is compatible with β-reduction. We then closely analyze some common factorization schemas for the λ-calculus.
Concretely, we apply our technique to diverse extensions of the λ-calculus, among which de' Liguoro and Piperno’s non-deterministic λ-calculus and - for call-by-value - Carraro and Guerrieri’s shuffling calculus. For both calculi the literature contains factorization theorems. In both cases, we give a new proof which is neat, simpler than the original, and strikingly shorter.

BibTeX - Entry

@InProceedings{accattoli_et_al:LIPIcs:2021:13440,
  author =	{Beniamino Accattoli and Claudia Faggian and Giulio Guerrieri},
  title =	{{Factorize Factorization}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{6:1--6:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Christel Baier and Jean Goubault-Larrecq},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13440},
  URN =		{urn:nbn:de:0030-drops-134407},
  doi =		{10.4230/LIPIcs.CSL.2021.6},
  annote =	{Keywords: Lambda Calculus, Rewriting, Reduction Strategies, Factorization}
}

Keywords: Lambda Calculus, Rewriting, Reduction Strategies, Factorization
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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