2026-07-21T12:58:01Z https://drops.dagstuhl.de/oai

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Differential Logical Relations, Part I: The Simply-Typed Case (Track B: Automata, Logic, Semantics, and Theory of Programming) Dal Lago, Ugo Gavazzo, Francesco Yoshimizu, Akira Logical Relations lambda-Calculus Program Equivalence Semantics 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ugo Dal Lago and Francesco Gavazzo and Akira Yoshimizu 2019 Is Part Of LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2019.111 urn:nbn:de:0030-drops-106879 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.111 eng https://creativecommons.org/licenses/by/3.0/legalcode