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Finitary Corecursion for the Infinitary Lambda Calculus

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Abstract

Kurz et al. have recently shown that infinite lambda-trees with finitely many free variables modulo alpha-equivalence form a final coalgebra for a functor on the category of nominal sets. Here we investigate the rational fixpoint of that functor. We prove that it is formed by all rational lambda-trees, i.e. those lambda-trees which have only finitely many subtrees (up to isomorphism). This yields a corecursion principle that allows the definition of operations such as substitution on rational lambda-trees.

BibTeX - Entry

@InProceedings{milius_et_al:LIPIcs:2015:5543,
  author =	{Stefan Milius and Thorsten Wi{\ss}mann},
  title =	{{Finitary Corecursion for the Infinitary Lambda Calculus}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{336--351},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Lawrence S. Moss and Pawel Sobocinski},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5543},
  URN =		{urn:nbn:de:0030-drops-55436},
  doi =		{10.4230/LIPIcs.CALCO.2015.336},
  annote =	{Keywords: rational trees, infinitary lambda calculus, coinduction}
}

Keywords: rational trees, infinitary lambda calculus, coinduction
Seminar: 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)
Issue date: 2015
Date of publication: 2015


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