On Generalized Metric Spaces for the Simply Typed LambdaCalculus (Extended Version)
Abstract
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 higherorder 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 higherorder types.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 DOI:
 10.48550/arXiv.2104.13324
 arXiv:
 arXiv:2104.13324
 Bibcode:
 2021arXiv210413324P
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Programming Languages;
 Mathematics  Logic;
 D.3.1;
 F.3.1;
 F.3.2