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.FSCD.2022.4
URN: urn:nbn:de:0030-drops-162851
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16285/
Dal Lago, Ugo ;
Honsell, Furio ;
Lenisa, Marina ;
Pistone, Paolo
On Quantitative Algebraic Higher-Order Theories
Abstract
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures which naturally emerge from Combinatory Logic and the λ-calculus. First of all, we show that the framework is indeed applicable to those structures, and give soundness and completeness results. Then, we prove some negative results clearly delineating to which extent categories of metric spaces can be models of such theories. We conclude by giving several examples of non-trivial higher-order quantitative algebras.
BibTeX - Entry
@InProceedings{dallago_et_al:LIPIcs.FSCD.2022.4,
author = {Dal Lago, Ugo and Honsell, Furio and Lenisa, Marina and Pistone, Paolo},
title = {{On Quantitative Algebraic Higher-Order Theories}},
booktitle = {7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
pages = {4:1--4:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-233-4},
ISSN = {1868-8969},
year = {2022},
volume = {228},
editor = {Felty, Amy P.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16285},
URN = {urn:nbn:de:0030-drops-162851},
doi = {10.4230/LIPIcs.FSCD.2022.4},
annote = {Keywords: Quantitative Algebras, Lambda Calculus, Combinatory Logic, Metric Spaces}
}
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Keywords: |
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Quantitative Algebras, Lambda Calculus, Combinatory Logic, Metric Spaces |
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Collection: |
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7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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28.06.2022 |
