License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2021.21
URN: urn:nbn:de:0030-drops-143982
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14398/
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Kori, Mayuko ; Hasuo, Ichiro ; Katsumata, Shin-ya

Fibrational Initial Algebra-Final Coalgebra Coincidence over Initial Algebras: Turning Verification Witnesses Upside Down

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Abstract

The coincidence between initial algebras (IAs) and final coalgebras (FCs) is a phenomenon that underpins various important results in theoretical computer science. In this paper, we identify a general fibrational condition for the IA-FC coincidence, namely in the fiber over an initial algebra in the base category. Identifying (co)algebras in a fiber as (co)inductive predicates, our fibrational IA-FC coincidence allows one to use coinductive witnesses (such as invariants) for verifying inductive properties (such as liveness). Our general fibrational theory features the technical condition of stability of chain colimits; we extend the framework to the presence of a monadic effect, too, restricting to fibrations of complete lattice-valued predicates. Practical benefits of our categorical theory are exemplified by new "upside-down" witness notions for three verification problems: probabilistic liveness, and acceptance and model-checking with respect to bottom-up tree automata.

BibTeX - Entry

@InProceedings{kori_et_al:LIPIcs.CONCUR.2021.21,
  author =	{Kori, Mayuko and Hasuo, Ichiro and Katsumata, Shin-ya},
  title =	{{Fibrational Initial Algebra-Final Coalgebra Coincidence over Initial Algebras: Turning Verification Witnesses Upside Down}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14398},
  URN =		{urn:nbn:de:0030-drops-143982},
  doi =		{10.4230/LIPIcs.CONCUR.2021.21},
  annote =	{Keywords: initial algebra, final coalgebra, fibration, category theory}
}

Keywords: initial algebra, final coalgebra, fibration, category theory
Collection: 32nd International Conference on Concurrency Theory (CONCUR 2021)
Issue Date: 2021
Date of publication: 13.08.2021

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