A Distribution Semantics for Probabilistic Term Rewriting

TL;DR

This paper introduces a new distribution semantics for probabilistic term rewriting systems, enabling the modeling and efficient computation of reduction probabilities, with potential for enhanced expressive power.

Contribution

It proposes a novel distribution semantics for probabilistic rewriting systems and methods to compute reduction probabilities efficiently.

Findings

Defined a distribution semantics for probabilistic term rewriting

Developed a method to compute explanations for reductions

Illustrated the approach with multiple examples

Abstract

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.