* [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 HomotopyTypeTheoryemail@example.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, back to index
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
Discussion of Homotopy Type Theory and Univalent Foundations
Archives are clonable: git clone --mirror http://inbox.vuxu.org/hott
Example config snippet for mirrors
Newsgroup available over NNTP:
AGPL code for this site: git clone https://public-inbox.org/public-inbox.git