Verified Density Compilation for a Probabilistic Programming Language

Author:

Tassarotti Joseph1ORCID,Tristan Jean-Baptiste2ORCID

Affiliation:

1. New York University, USA

2. Amazon Web Services, USA

Abstract

This paper presents ProbCompCert, a compiler for a subset of the Stan probabilistic programming language (PPL), in which several key compiler passes have been formally verified using the Coq proof assistant. Because of the probabilistic nature of PPLs, bugs in their compilers can be difficult to detect and fix, making verification an interesting possibility. However, proving correctness of PPL compilation requires new techniques because certain transformations performed by compilers for PPLs are quite different from other kinds of languages. This paper describes techniques for verifying such transformations and their application in ProbCompCert. In the course of verifying ProbCompCert, we found an error in the Stan language reference manual related to the semantics and implementation of a key language construct.

Funder

NSF

Publisher

Association for Computing Machinery (ACM)

Subject

Safety, Risk, Reliability and Quality,Software

Reference38 articles.

1. AcMC 2

2. Reactive probabilistic programming

3. Matthew R. Becker. 2016. NUTS Sampler Broken (stan-dev/stan issue #2178). https://github.com/stan-dev/stan/issues/2178 Matthew R. Becker. 2016. NUTS Sampler Broken (stan-dev/stan issue #2178). https://github.com/stan-dev/stan/issues/2178

4. Michael Betancourt. 2018. A Conceptual Introduction to Hamiltonian Monte Carlo. arxiv:1701.02434. Michael Betancourt. 2018. A Conceptual Introduction to Hamiltonian Monte Carlo. arxiv:1701.02434.

5. Sooraj Bhat , Johannes Borgström , Andrew D. Gordon , and Claudio Russo . 2013. Deriving Probability Density Functions from Probabilistic Functional Programs . In Tools and Algorithms for the Construction and Analysis of Systems, Nir Piterman and Scott A . Smolka (Eds.). Springer Berlin Heidelberg , Berlin, Heidelberg . 508–522. isbn:978-3-642-36742-7 Sooraj Bhat, Johannes Borgström, Andrew D. Gordon, and Claudio Russo. 2013. Deriving Probability Density Functions from Probabilistic Functional Programs. In Tools and Algorithms for the Construction and Analysis of Systems, Nir Piterman and Scott A. Smolka (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg. 508–522. isbn:978-3-642-36742-7

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