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.
On Quantitative Algebraic Higher-Order Theories / Ugo Dal Lago; Furio Honsell; Marina Lenisa; Paolo Pistone. - ELETTRONICO. - 228:(2022), pp. 4.1-4.18. (Intervento presentato al convegno 7th International Conference on Formal Structures for Computation and Deduction, FSCD 2022. tenutosi a Haifa, Israel nel August 2-5, 2022.) [10.4230/lipics.fscd.2022.4].
On Quantitative Algebraic Higher-Order Theories
Ugo Dal Lago
;Paolo Pistone
2022
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.| File | Dimensione | Formato | |
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