On Generalized Metric Spaces for the Simply Typed Lambda-Calculus

Paolo Pistone (1, 2)

1 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
2 FOCUS - Foundations of Component-based Ubiquitous Systems

Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way. However, the application of generalized metrics to higher-order languages like the simply typed lambda calculus has so far proved unsatisfactory. In this paper we investigate a new approach to the construction of cartesian closed categories of generalized metric spaces. Our starting point is a quantitative semantics based on a generalization of usual logical relations. Within this setting, we show that several families of generalized metrics provide ways to extend the Euclidean metric to all higher-order types.

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

Paolo Pistone. On Generalized Metric Spaces for the Simply Typed Lambda-Calculus. LICS 2021 - 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2021, Rome, Italy. pp.1-14, ⟨10.1109/LICS52264.2021.9470696⟩. ⟨hal-03346950⟩