License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
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DOI: 10.4230/LIPIcs.RTA.2012.117
URN: urn:nbn:de:0030-drops-34889
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Bonelli, Eduardo ; Kesner, Delia ; Lombardi, Carlos ; Rios, Alejandro

Normalisation for Dynamic Pattern Calculi

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The Pure Pattern Calculus (PPC) extends the lambda-calculus, as well as the family of algebraic pattern calculi, with first-class patterns; that is, patterns can be passed as arguments, evaluated and returned as results. The notion of matching failure of the PPC not only provides a mechanism to define functions by pattern matching on cases but also supplies PPC with parallel-or-like, non-sequential behaviour. Therefore, devising normalising strategies for PPC to obtain well-behaved implementations turns out to be challenging.

This paper focuses on normalising reduction strategies for PPC. We define a (multistep) strategy and show that it is normalising. The strategy generalises the leftmost-outermost strategy for lambda-calculus and is strictly finer than parallel-outermost. The normalisation proof is based on the notion of necessary set of redexes, a generalisation of the notion of needed redex encompassing
non-sequential reduction systems.

BibTeX - Entry

  author =	{Eduardo Bonelli and Delia Kesner and Carlos Lombardi and Alejandro Rios},
  title =	{{Normalisation for Dynamic Pattern Calculi}},
  booktitle =	{23rd International Conference on Rewriting Techniques and Applications (RTA'12) },
  pages =	{117--132},
  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 =		{},
  URN =		{urn:nbn:de:0030-drops-34889},
  doi =		{10.4230/LIPIcs.RTA.2012.117},
  annote =	{Keywords: Pattern calculi, reduction strategies, sequentiality, neededness}

Keywords: Pattern calculi, reduction strategies, sequentiality, neededness
Collection: 23rd International Conference on Rewriting Techniques and Applications (RTA'12)
Issue Date: 2012
Date of publication: 29.05.2012

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