eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-06-28
4:1
4:18
10.4230/LIPIcs.FSCD.2022.4
article
On Quantitative Algebraic Higher-Order Theories
Dal Lago, Ugo
1
Honsell, Furio
2
Lenisa, Marina
2
Pistone, Paolo
1
Department of Computer Science and Engineering, University of Bologna, Italy
Department of Mathematical Sciences, Informatics and Physics, University of Udine, Italy
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol228-fscd2022/LIPIcs.FSCD.2022.4/LIPIcs.FSCD.2022.4.pdf
Quantitative Algebras
Lambda Calculus
Combinatory Logic
Metric Spaces