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.
2022
7th International Conference on Formal Structures for Computation and Deduction, FSCD 2022, August 2-5, 2022, Haifa, Israel.
1
18
Ugo Dal Lago, Furio Honsell, Marina Lenisa, Paolo Pistone (2022). On Quantitative Algebraic Higher-Order Theories [10.4230/lipics.fscd.2022.4].
Ugo Dal Lago; Furio Honsell; Marina Lenisa; Paolo Pistone
File in questo prodotto:
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.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/904334
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? ND
social impact