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Nested Fixpoints – A Coalgebraic View of Parametric Dataypes

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conference contribution
posted on 19.05.2015, 11:05 by Paula G. Severi, Alexande Kurz, Daniela Petrisan, Fer-Jan de Vries, Alberto Pardo
The question addressed in this paper is how to correctly approximate infinite data given by systems of simultaneous corecursive definitions. We devise a categorical framework for reasoning about reg- ular datatypes, that is, dataypes closed under products, coproducts and fixpoints. We argue that the right methodology is on one hand coalge- braic (to deal with possible non-termination and infinite data) and on the other hand 2-categorical (to deal with parameters in a disciplined manner). We prove a coalgebraic version of Bekic lemma that allows us to reduce simultaneous fixpoints to a single fix point. Thus a possibly in- finite object of interest is regarded as a final coalgebra of a many-sorted polynomial functor and can be seen as a limit of finite approximants. As an application, we prove correctness of a generic function that calculates the approximants on a large class of data types.

History

Citation

Leibniz International Proceedings in Informatics series, 2015, pp. 205-220

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Computer Science

Source

CALCO 2015 (6th Conference on Algebra and Coalgebra in Computer Science), Nijmegen, The Netherlands

Version

VoR (Version of Record)

Published in

Leibniz International Proceedings in Informatics series

Publisher

Schloss Dagstuhl Leibniz-Zentrum für Informatik

issn

1868-8969

Copyright date

2015

Available date

03/08/2016

Publisher version

http://drops.dagstuhl.de/opus/volltexte/2015/5535/

Temporal coverage: start date

24/06/2015

Temporal coverage: end date

26/06/2015

Language

en

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