ProbLog and applicative probabilistic programming

Probabilistic Programming Languages (PPLs) have a long history in both the functional (e.g., Anglican) and logic programming (e.g., ProbLog) paradigms. Unfortunately these efforts have been conducted mostly in isolation and little is known about the correspondences between the two approaches or their relative merits. In this work we establish a common ground for both approaches in terms of algebraic models of probabilistic computation. It is already well-known that functional PPLs conform to the monadic model. We show that ProbLog's flavour of probabilistic computation is restricted to the applicative functor interface. This means that functional PPLs afford greater expressivity in terms of dynamic program structure, while ProbLog programs are inherently more amenable to static analysis and thus afford faster inference. We believe that this insight opens up a number of interesting cross-fertilisation opportunities: - For Probabilistic Functional Languages: identifying applicative fragments in monadic programs can lead to more performant inference techniques. - For Probabilistic Logic Languages: characterising advanced features (e.g., those of ProbLog2) in terms of algebraic models. We invite you to explore these promising avenues with us.