Normalisation for dynamic pattern calculi

Eduardo Bonelli, Delia Kesner, Carlos Lombardi, Alejandro Ríos

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

The Pure Pattern Calculus (PPC) [10, 11] extends the λ-calculus, as well as the family of algebraic pattern calculi [20, 6, 12], with first-class patterns i.e. patterns can be passed as arguments, evaluated and returned as results. The notion of matching failure of PPC in [11] 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 λ-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.

Original languageEnglish
Title of host publication23rd International Conference on Rewriting Techniques and Applications, RTA 2012
Pages117-132
Number of pages16
DOIs
StatePublished - 2012
Event23rd International Conference on Rewriting Techniques and Applications, RTA 2012 - Nagoya, Japan
Duration: 30 May 20121 Jun 2012

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume15
ISSN (Print)1868-8969

Conference

Conference23rd International Conference on Rewriting Techniques and Applications, RTA 2012
Country/TerritoryJapan
CityNagoya
Period30/05/121/06/12

Keywords

  • Neededness
  • Pattern calculi
  • Reduction strategies
  • Sequentiality

Fingerprint

Dive into the research topics of 'Normalisation for dynamic pattern calculi'. Together they form a unique fingerprint.

Cite this