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DOI: 10.4230/LIPIcs.CSL.2017.39

Taylor Expansion, lambda-Reduction and Normalization

Authors: Lionel Vaux

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

We introduce a notion of reduction on resource vectors, i.e. infinite linear combinations of resource lambda-terms. The latter form the multilinear fragment of the differential lambda-calculus introduced by Ehrhard and Regnier, and resource vectors are the target of the Taylor expansion of lambda-terms. We show that the reduction of resource vectors contains the image, through Taylor expansion, of beta-reduction in the algebraic lambda-calculus, i.e. lambda-calculus extended with weighted sums: in particular, Taylor expansion and normalization commute. We moreover exhibit a class of algebraic lambda-terms, having a normalizable Taylor expansion, subsuming both arbitrary pure lambda-terms, and normalizable algebraic lambda-terms. For these, we prove the commutation of Taylor expansion and normalization in a more denotational sense, mimicking the Böhm tree construction.

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Lionel Vaux. Taylor Expansion, lambda-Reduction and Normalization. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 39:1-39:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{vaux:LIPIcs.CSL.2017.39,
  author =	{Vaux, Lionel},
  title =	{{Taylor Expansion, lambda-Reduction and Normalization}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{39:1--39:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.39},
  URN =		{urn:nbn:de:0030-drops-76948},
  doi =		{10.4230/LIPIcs.CSL.2017.39},
  annote =	{Keywords: lambda-calculus, non-determinism, normalization, denotational semantics}
}

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Taylor Expansion, lambda-Reduction and Normalization

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