From: Bas Spitters <email@example.com> To: homotopytypetheory <firstname.lastname@example.org>, Constructive News <email@example.com> Subject: [HoTT] Synthetic topology in Homotopy Type Theory for probabilistic programming Date: Mon, 30 Dec 2019 19:05:40 +0100 Message-ID: <CAOoPQuR4ttw71bPEA+xtXZ__Q5kKFGRqgJVgTA=2PmLc5=d5Lw@mail.gmail.com> (raw) We have a new paper on the arxiv. Comments, suggestions and questions are very welcome. Synthetic topology in Homotopy Type Theory for probabilistic programming Martin E. Bidlingmaier, Florian Faissole, Bas Spitters The ALEA Coq library formalizes measure theory based on a variant of the Giry monad on the category of sets. This enables the interpretation of a probabilistic programming language with primitives for sampling from discrete distributions. However, continuous distributions have to be discretized because the corresponding measures cannot be defined on all subsets of their carriers. This paper proposes the use of synthetic topology to model continuous distributions for probabilistic computations in type theory. We study the initial σ-frame and the corresponding induced topology on arbitrary sets. Based on these intrinsic topologies we define valuations and lower integrals on sets, and prove versions of the Riesz and Fubini theorems. We then show how the Lebesgue valuation, and hence continuous distributions, can be constructed. -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheoryfirstname.lastname@example.org. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/CAOoPQuR4ttw71bPEA%2BxtXZ__Q5kKFGRqgJVgTA%3D2PmLc5%3Dd5Lw%40mail.gmail.com.
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