A Typed Lambda-Calculus for Establishing Trust in Probabilistic Programs

The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said to compute the correct result, we often have quite strong expectations about the frequency with which it should return certain outputs. In these cases, trust as a generalisation of correctness fares better. One way to understand it is to say that a probabilistic computational process is trustworthy if the frequency of its outputs is compliant with a probability distribution which models its expected behaviour.