On Generalized Metric Spaces for the Simply Typed Lambda-Calculus

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 hig...

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Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 14
Main Author: Pistone, Paolo
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Calculus
Cognition
Computer science
Euclidean distance
Extraterrestrial measurements
Semantics
Online Access:Get full text
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Summary: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.
DOI:10.1109/LICS52264.2021.9470696