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.
Ugo Dal Lago, Furio Honsell, Marina Lenisa, Paolo Pistone (2022). On Quantitative Algebraic Higher-Order Theories [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 | |
|---|---|---|---|
|
fscd2022.pdf
accesso aperto
Tipo:
Versione (PDF) editoriale
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione
802.31 kB
Formato
Adobe PDF
|
802.31 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
