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DOI: 10.4230/LIPIcs.LICS.2026.71

Verifying Exact Samplers for Continuous Distributions with a Discrete Program Logic

Authors: Markus de Medeiros, Puming Liu, Kwing Hei Li, Alejandro Aguirre, Lars Birkedal, and Joseph Tassarotti

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

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.

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Markus de Medeiros, Puming Liu, Kwing Hei Li, Alejandro Aguirre, Lars Birkedal, and Joseph Tassarotti. Verifying Exact Samplers for Continuous Distributions with a Discrete Program Logic. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 71:1-71:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{demedeiros_et_al:LIPIcs.LICS.2026.71,
  author =	{de Medeiros, Markus and Liu, Puming and Li, Kwing Hei and Aguirre, Alejandro and Birkedal, Lars and Tassarotti, Joseph},
  title =	{{Verifying Exact Samplers for Continuous Distributions with a Discrete Program Logic}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{71:1--71:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.71},
  URN =		{urn:nbn:de:0030-drops-268584},
  doi =		{10.4230/LIPIcs.LICS.2026.71},
  annote =	{Keywords: Probabilistic Programming, Separation Logic, Formal Verification}
}

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DOI: 10.4230/LIPIcs.ICALP.2018.113

Almost Sure Productivity

Authors: Alejandro Aguirre, Gilles Barthe, Justin Hsu, and Alexandra Silva

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract

We introduce Almost Sure Productivity (ASP), a probabilistic generalization of the productivity condition for coinductively defined structures. Intuitively, a probabilistic coinductive stream or tree is ASP if it produces infinitely many outputs with probability 1. Formally, we define ASP using a final coalgebra semantics of programs inspired by Kerstan and König. Then, we introduce a core language for probabilistic streams and trees, and provide two approaches to verify ASP: a syntactic sufficient criterion, and a decision procedure by reduction to model{-}checking LTL formulas on probabilistic pushdown automata.

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Alejandro Aguirre, Gilles Barthe, Justin Hsu, and Alexandra Silva. Almost Sure Productivity. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 113:1-113:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{aguirre_et_al:LIPIcs.ICALP.2018.113,
  author =	{Aguirre, Alejandro and Barthe, Gilles and Hsu, Justin and Silva, Alexandra},
  title =	{{Almost Sure Productivity}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{113:1--113:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.113},
  URN =		{urn:nbn:de:0030-drops-91174},
  doi =		{10.4230/LIPIcs.ICALP.2018.113},
  annote =	{Keywords: Coinduction, Probabilistic Programming, Productivity}
}

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Verifying Exact Samplers for Continuous Distributions with a Discrete Program Logic

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Almost Sure Productivity

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