Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we consider systems that combine traditional rewriting rules with probabilities. Then, we define a novel "distribution semantics" for such systems that can be used to model the probability of reducing a term to some value. We also show how to compute a set of "explanations" for a given reduction, which can be used to compute its probability in a more efficient way. Finally, we illustrate our approach with several examples and outline a couple of extensions that may prove useful to improve the expressive power of probabilistic rewrite systems.

翻译：概率编程因其能够描述具有一定不确定性的问题而日益流行。在本工作中，我们关注项重写这一经典的计算形式化方法。具体而言，我们研究将传统重写规则与概率相结合的系统。为此，我们为此类系统定义了一种新颖的"分布语义"，可用于建模项归约为某个值的概率。我们还展示了如何为给定归约计算一组"解释"，这可用于更高效地计算其概率。最后，我们通过若干示例阐述所提出的方法，并概述了几种可能有助于提升概率重写系统表达能力的扩展方向。