As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages that treat probability distributions as primitive datatypes. Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power. In this paper, we present a probabilistic language, called λ_O, which uniformly supports all kinds of probability distributions -- discrete distributions, continuous distributions, and even those belonging to neither group. Its mathematical basis is sampling functions, i.e., mappings from the unit interval (0.0,1.0] to probability domains. We also briefly describe the implementation of λ_O as an extension of Objective CAML and demonstrate its practicality with three applications in robotics: robot localization, people tracking, and robotic mapping. All experiments have been carried out with real robots.

30 pages

*Computer Science Department, Stanford University

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