Inference algorithms for probabilistic programming are complex imperative programs with many moving parts. Efficient inference often requires customising an algorithm to a particular probabilistic model or problem, sometimes called inference programming. Most inference frameworks are implemented in languages that lack a disciplined approach to side effects, which can result in monolithic implementations where the structure of the algorithms is obscured and inference programming is hard. Functional programming with typed effects offers a more structured and modular foundation for programmable inference, with monad transformers being the primary structuring mechanism explored to date. This paper presents an alternative approach to inference programming based on algebraic effects. Using effect signatures to specify the key operations of the algorithms, and effect handlers to modularly interpret those operations for specific variants, we develop two abstract algorithms, or inference patterns, representing two important classes of inference: Metropolis-Hastings and particle filtering. We show how our approach reveals the algorithms' high-level structure, and makes it easy to tailor and recombine their parts into new variants. We implement the two inference patterns as a Haskell library, and discuss the pros and cons of algebraic effects vis-a-vis monad transformers as a structuring mechanism for modular imperative algorithm design.

翻译：概率编程的推理算法是包含众多组件的复杂命令式程序。高效推理通常需要针对特定概率模型或问题定制算法，这被称为推理编程。大多数推理框架使用缺乏对副作用进行严格处理的语言实现，导致算法结构不透明且推理编程困难。带类型化效果的函数式编程为可编程推理提供了更结构化的模块化基础，其中单子变换器是目前主要探索的结构化机制。本文提出一种基于代数效果的推理编程替代方案。通过使用效果签名指定算法的关键操作，并利用效果处理器模块化解释特定变体的操作，我们开发了两种抽象算法（即推理模式），分别代表Metropolis-Hastings和粒子滤波这两类重要推理。研究展示了该方法如何揭示算法的高层结构，并使得算法组件的定制与重组以形成新变体变得简单。我们将这两种推理模式实现为Haskell库，并讨论了代数效果与单子变换器作为模块化命令式算法设计结构机制的优缺点。