Thomas Ehrhard - Differentials and distances in probabilistic coherence spaces

lmcs:6511 - Logical Methods in Computer Science, August 8, 2022, Volume 18, Issue 3 - https://doi.org/10.46298/lmcs-18(3:2)2022
Differentials and distances in probabilistic coherence spaces

Authors: Thomas Ehrhard

    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.


    Volume: Volume 18, Issue 3
    Published on: August 8, 2022
    Accepted on: February 10, 2022
    Submitted on: May 27, 2020
    Keywords: Computer Science - Logic in Computer Science,D.3.1,F.3.2
    Fundings :
      Source : OpenAIRE Research Graph
    • Probabilistic program semantics; Funder: French National Research Agency (ANR); Code: ANR-19-CE48-0014

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