2026-07-22T22:17:57Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16285 2024-03-06T10:57:08Z ddc:004 open_access

On Quantitative Algebraic Higher-Order Theories Dal Lago, Ugo Honsell, Furio Lenisa, Marina Pistone, Paolo Quantitative Algebras Lambda Calculus Combinatory Logic Metric Spaces 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ugo Dal Lago and Furio Honsell and Marina Lenisa and Paolo Pistone 2022 Is Part Of LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2022.4 urn:nbn:de:0030-drops-162851 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.4 eng https://creativecommons.org/licenses/by/4.0/legalcode