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arXiv · 2104.13324

On Generalized Metric Spaces for the Simply Typed Lambda-Calculus (Extended Version)

Paolo Pistone
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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 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.

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Paolo Pistone. 2021-04-27. On Generalized Metric Spaces for the Simply Typed Lambda-Calculus (Extended Version). https://arxiv.org/abs/2104.13324

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