* [HoTT] Synthetic topology in Homotopy Type Theory for probabilistic programming
@ 2019-12-30 18:05 Bas Spitters
0 siblings, 0 replies; only message in thread
From: Bas Spitters @ 2019-12-30 18:05 UTC (permalink / raw)
To: homotopytypetheory, Constructive News
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 HomotopyTypeTheory+unsubscribe@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/CAOoPQuR4ttw71bPEA%2BxtXZ__Q5kKFGRqgJVgTA%3D2PmLc5%3Dd5Lw%40mail.gmail.com.
^ permalink raw reply [flat|nested] only message in thread
only message in thread, other threads:[~2019-12-30 18:05 UTC | newest]
Thread overview: (only message) (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2019-12-30 18:05 [HoTT] Synthetic topology in Homotopy Type Theory for probabilistic programming Bas Spitters
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).