Differential Logical Relations, Part I: The Simply-Typed Case (Long Version) release_n7nnwhirfjahtgjzog7yyu2vmq

by Ugo Dal Lago, Francesco Gavazzo, Akira Yoshimizu

Released as a article .

2019  

Abstract

We introduce a new form of logical relation which, in the spirit of metric relations, allows us to assign each pair of programs a quantity measuring their distance, rather than a boolean value standing for their being equivalent. The novelty of differential logical relations consists in measuring the distance between terms not (necessarily) by a numerical value, but by a mathematical object which somehow reflects the interactive complexity, i.e. the type, of the compared terms. We exemplify this concept in the simply-typed lambda-calculus, and show a form of soundness theorem. We also see how ordinary logical relations and metric relations can be seen as instances of differential logical relations. Finally, we show that differential logical relations can be organised in a cartesian closed category, contrarily to metric relations, which are well-known not to have such a structure, but only that of a monoidal closed category.
In text/plain format

Archived Files and Locations

application/pdf  739.5 kB
file_cvjxyxxkore67dzho4ndxrjaeu
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2019-04-27
Version   v1
Language   en ?
arXiv  1904.12137v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: fd5719b7-f728-4119-a7e7-03103ee93a0c
API URL: JSON