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：概率编程的推断算法是包含许多移动部件的复杂命令式程序。高效推断通常需要针对特定概率模型或问题定制算法，有时称为推断编程。大多数推断框架以缺乏对副作用进行规范处理的语言实现，这可能导致算法结构模糊且推断编程困难的单体式实现。带有类型化效果的函数式编程为可编程推断提供了结构更清晰且模块化的基础，其中单子变换器是目前探索的主要结构化机制。本文提出了一种基于代数效果（algebraic effects）的推断编程替代方法。通过使用效果签名（effect signatures）来指定算法的关键操作，并利用效果处理器（effect handlers）模块化地解释这些操作以适配特定变体，我们开发了两种抽象算法（即推断模式），代表两类重要的推断方法：Metropolis-Hastings和粒子滤波。我们展示了该方法如何揭示算法的高层结构，并使得轻松定制和重组其组件以生成新变体成为可能。我们将这两种推断模式实现为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化机制的优缺点。