A lambda-calculus foundation for universal probabilistic programming

@article{Borgstrm2015ALF,
  title={A lambda-calculus foundation for universal probabilistic programming},
  author={J. Borgstr{\"o}m and Ugo Dal Lago and A. D. Gordon and M. Szymczak},
  journal={Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming},
  year={2015}
}
We develop the operational semantics of an untyped probabilistic λ-calculus with continuous distributions, and both hard and soft constraints,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 λ-calculus to a continuous setting via creating a measure space on terms and defining step-indexed approximations. We prove equivalence of big-step and small-step formulations of… Expand
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