@inproceedings{
  Heunen_2017,
  author = {Heunen, Chris and Kammar, Ohad and Staton, Sam and Yang, Hongseok},
  title = {A Convenient Category for Higher-Order Probability Theory},
  year = {2017},
  isbn = {9781509030187},
  publisher = {IEEE Press},
  abstract = {Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed.Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.},
  booktitle = {Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science},
  articleno = {77},
  numpages = {12},
  location = {Reykjav\'{\i}k, Iceland},
  series = {LICS '17}
}