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Sat 23 Jan 2016 14:00 - 14:20 at Room St Petersburg II - Session 3 Chair(s): Mitchell Wand

We develop the operational semantics of a probabilistic lambda- calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution is to adapt the classic operational semantics of lambda-calculus to the continuous case, via creating a measure space on terms and defining step-indexed approximations. We prove equivalence of big-step and small-step formulations of this distributional semantics. Our second contribution is to formalize the implementation technique of trace MCMC for our calculus and to show correctness. A key step is defining a sampling semantics of a term as a function from a trace of random samples to a value, and showing that the distribution induced by integrating over all traces equals the distributional semantics. Another step is defining sufficient conditions for the distribution induced by trace MCMC to converge to the distributional semantics. To the best of our knowledge, this is the first rigorous correctness proof for trace MCMC for a higher-order functional language.

Sat 23 Jan

pps-2016
14:00 - 15:30: PPS 2016 - Session 3 at Room St Petersburg II
Chair(s): Mitchell WandNortheastern University
pps-201614:00 - 14:20
Talk
Johannes BorgströmUppsala University, Ugo Dal LagoUniversity of Bologna, Andrew D. GordonMicrosoft Research and University of Edinburgh, Marcin SzymczakUniversity of Edinburgh
Pre-print
pps-201614:20 - 14:30
Meeting
pps-201614:30 - 14:50
Talk
Leonidas LampropoulosUniversity of Pennsylvania, Benjamin C. PierceUniversity of Pennsylvania, Cătălin HriţcuINRIA Paris, John HughesChalmers University of Technology, Zoe ParaskevopoulouPrinceton University, Li-yao XiaENS Paris
Pre-print
pps-201614:50 - 15:00
Meeting
pps-201615:00 - 15:20
Talk
Sam StatonUniversity of Oxford, Hongseok YangUniversity of Oxford, UK, Chris HeunenUniversity of Edinburgh, Ohad KammarUniversity of Cambridge, Frank WoodUniversity of Oxford
Pre-print
pps-201615:20 - 15:30
Meeting