Computable Exchangeable Sequences Have Computable de Finetti Measures

  • Cameron E. Freer
  • Daniel M. Roy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5635)


We prove a uniformly computable version of de Finetti’s theorem on exchangeable sequences of real random variables. In the process, we develop machinery for computably recovering a distribution from its sequence of moments, which suffices to prove the theorem in the case of (almost surely) continuous directing random measures. In the general case, we give a proof inspired by a randomized algorithm which succeeds with probability one. Finally, we show how, as a consequence of the main theorem, exchangeable stochastic processes in probabilistic functional programming languages can be rewritten as procedures that do not use mutation.


de Finetti exchangeability computable probability theory probabilistic programming languages mutation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Cameron E. Freer
    • 1
  • Daniel M. Roy
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyUSA
  2. 2.Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of TechnologyUSA

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