PRISM revisited: Declarative implementation of a probabilistic programming language using multi-prompt delimited control

Abstract

PRISM is a probabilistic programming language based on Prolog, augmented with primitives to represent probabilistic choice. It is implemented using a combination of low level support from a modified version of B-Prolog, source level program transformation, and libraries for inference and learning implemented in C. More recently, developers working with functional programming languages have taken the approach of embedding probabilistic primitives into an existing language, with little or no modification to the host language, often by using delimited continuations. Captured continuations represent pieces of the probabilistic program which can be manipulated to achieve a great variety of computational effects useful for inference. In this paper, I will describe an approach based on delimited control operators recently introduced into SWI Prolog. These are used to create a system of nested effect handlers which together implement a core functionality of PRISM—the building of explanation graphs—entirely in Prolog and using an order of magnitude less code. Other declarative programming tools, such as constraint logic programming, are used to implement tools for inference, such as the inside-outside and EM algorithms, lazy best-first explanation search, and MCMC samplers. By embedding the functionality of PRISM into SWI Prolog, users gain access to its rich libraries and development environment. By expressing the functionality of PRISM in a small amount of pure, high-level Prolog, this implementation facilitates further experimentation with the mechanisms of probabilistic logic programming, including new probabilistic modelling features and inference algorithms, such as variational inference in models with real-valued variables.