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: https://drops.dagstuhl.de/opus/volltexte/2021/14398/
Kori, Mayuko ;
Hasuo, Ichiro ;
Katsumata, Shin-ya
Fibrational Initial Algebra-Final Coalgebra Coincidence over Initial Algebras: Turning Verification Witnesses Upside Down
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: |
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initial algebra, final coalgebra, fibration, category theory |
Collection: |
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32nd International Conference on Concurrency Theory (CONCUR 2021) |
Issue Date: |
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2021 |
Date of publication: |
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13.08.2021 |