Paper: Verifying Exact Samplers for Continuous Distributions with a Discrete Program Logic (at LICS 2026)
Open access: https://doi.org/10.4230/LIPIcs.LICS.2026.71
Abstract
Most implementations of sampling algorithms for continuous distributions use floating-point numbers, which introduce round-off errors and approximations. These errors can be difficult to analyze, and can cause security issues when used in algorithms for differential privacy. An alternative is to use exact sampling algorithms based on computable reals, which can lazily generate the digits of a continuous sample to arbitrary precision. However, these algorithms are intricate, and implementing and using them involves a combination of semantically challenging language features, such as probabilistic choice, higher-order functions, and dynamically-allocated mutable state. In this paper we present Continuous-Eris, a higher-order separation logic for verifying the correctness of exact sampling algorithms for computable distributions. To demonstrate Continuous-Eris, we verify the correctness of computable samplers for the uniform, Gaussian, and Laplace distributions, as well as a library for exact real arithmetic for working with generated samples. All of the results in this paper have been verified in the Rocq proof assistant.
BibTeX
@InProceedings{MedeirosLiuLiAguirr-VerifyingExactSampl,
author = {Markus de Medeiros and Puming Liu and Kwing Hei Li and Alejandro Aguirre and Lars Birkedal and Joseph Tassarotti},
title = {Verifying Exact Samplers for Continuous Distributions with a Discrete Program Logic},
booktitle = {Proceedings of the Forty-First Annual Symposium on Logic in Computer Science (LICS 2026)},
year = {2026},
month = {July},
pages = {71:1--71:28},
location = {Lisbon, Portugal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
doi = {10.4230/LIPIcs.LICS.2026.71}
}