2026-07-28T05:47:30Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:10524 2024-03-06T10:46:08Z ddc:004 open_access

Differentials and Distances in Probabilistic Coherence Spaces Ehrhard, Thomas Denotational semantics probabilistic coherence spaces differentials of programs In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives allow to compute the expectation of execution time in the weak head reduction of probabilistic PCF (pPCF). Next we apply a general notion of "local" differential of morphisms to the proof of a Lipschitz property of these morphisms allowing in turn to relate the observational distance on pPCF terms to a distance the model is naturally equipped with. This suggests that extending probabilistic programming languages with derivatives, in the spirit of the differential lambda-calculus, could be quite meaningful. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thomas Ehrhard 2019 Is Part Of LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2019.17 urn:nbn:de:0030-drops-105243 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.17 eng https://creativecommons.org/licenses/by/3.0/legalcode