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POPL 2019
Sun 13 - Sat 19 January 2019 Cascais, Portugal
Wed 16 Jan 2019 14:07 - 14:29 at Sala I - Probabilistic Programming and Semantics Chair(s): Justin Hsu

We give an adequate denotational semantics for languages with recursive higher-order types, continuous probability distributions, and soft constraints. These are expressive languages for building Bayesian models of the kinds used in computational statistics and machine learning. Among them are untyped languages, similar to Church and WebPPL, because our semantics allows recursive mixed-variance datatypes. Our semantics justifies important program equivalences including commutativity.

Our new semantic model is based on `quasi-Borel predomains’. These are a mixture of chain-complete partial orders (cpos) and quasi-Borel spaces. Quasi-Borel spaces are a recent model of probability theory that focuses on sets of admissible random elements. Probability is traditionally treated in cpo models using probabilistic powerdomains, but these are not known to be commutative on any class of cpos with higher order functions. By contrast, quasi-Borel predomains do support both a commutative probabilistic powerdomain and higher-order functions. As we show, quasi-Borel predomains form both a model of Fiore’s axiomatic domain theory and a model of Kock’s synthetic measure theory.

A Domain Theory for Statistical Probabilistic Programming - slides (popl-2019.pdf)2.35MiB

Wed 16 Jan

13:45 - 14:51: Research Papers - Probabilistic Programming and Semantics at Sala I
Chair(s): Justin HsuUniversity of Wisconsin-Madison, USA
POPL-2019-Research-Papers13:45 - 14:07
Maria I. GorinovaThe University of Edinburgh, Andrew D. GordonMicrosoft Research and University of Edinburgh, Charles SuttonUniversity of Edinburgh
Link to publication DOI Pre-print File Attached
POPL-2019-Research-Papers14:07 - 14:29
Matthijs VákárUniversity of Oxford, Ohad KammarUniversity of Edinburgh, Sam StatonUniversity of Oxford
Link to publication DOI Pre-print File Attached
POPL-2019-Research-Papers14:29 - 14:51
Feras SaadMassachusetts Institute of Technology, Marco Cusumano-TownerMIT-CSAIL, Ulrich SchaechtleMassachusetts Institute of Technology, USA, Martin RinardMassachusetts Institute of Technology, Vikash MansingkhaMIT
Link to publication DOI File Attached