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.2017.39
URN: urn:nbn:de:0030-drops-76948
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7694/
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Vaux, Lionel

Taylor Expansion, lambda-Reduction and Normalization

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LIPIcs-CSL-2017-39.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{vaux:LIPIcs:2017:7694,
  author =	{Lionel Vaux},
  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 =	{Valentin Goranko and Mads Dam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7694},
  URN =		{urn:nbn:de:0030-drops-76948},
  doi =		{10.4230/LIPIcs.CSL.2017.39},
  annote =	{Keywords: lambda-calculus, non-determinism, normalization, denotational semantics}
}

Keywords: lambda-calculus, non-determinism, normalization, denotational semantics
Collection: 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)
Issue Date: 2017
Date of publication: 16.08.2017

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