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DOI: 10.4230/LIPIcs.RTA.2012.22
URN: urn:nbn:de:0030-drops-34820
URL: http://drops.dagstuhl.de/opus/volltexte/2012/3482/

Accattoli, Beniamino ; Dal Lago, Ugo

On the Invariance of the Unitary Cost Model for Head Reduction

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Abstract

The lambda-calculus is a widely accepted computational model of higher-order functional programs, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda-terms to their normal form is typically studied by reasoning on concrete implementation algorithms. In this paper, we show that when head reduction is the underlying dynamics, the unitary cost model is indeed invariant. This improves on known results, which only deal with weak (call-by-value or call-by-name) reduction. Invariance is proved by way of a linear calculus of explicit substitutions, which allows to nicely decompose any head reduction step in the lambda-calculus into more elementary substitution steps, thus making the combinatorics of head-reduction easier to reason about. The technique is also a promising tool to attack what we see as the main open problem, namely understanding for which normalizing strategies the unitary cost model is invariant, if any.

BibTeX - Entry

@InProceedings{accattoli_et_al:LIPIcs:2012:3482,
  author =	{Beniamino Accattoli and Ugo Dal Lago},
  title =	{{On the Invariance of the Unitary Cost Model for Head Reduction}},
  booktitle =	{23rd International Conference on Rewriting Techniques and Applications (RTA'12) },
  pages =	{22--37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-38-5},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{15},
  editor =	{Ashish Tiwari},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3482},
  URN =		{urn:nbn:de:0030-drops-34820},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.RTA.2012.22},
  annote =	{Keywords: lambda calculus, cost models, explicit substitutions, implicit computational complexity}
}

Keywords: lambda calculus, cost models, explicit substitutions, implicit computational complexity
Seminar: 23rd International Conference on Rewriting Techniques and Applications (RTA'12)
Issue date: 2012
Date of publication: 15.05.2012


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