Formally Verified Samplers from Probabilistic Programs with Loops and Conditioning-Reference-Cited by-同舟云学术

Formally Verified Samplers from Probabilistic Programs with Loops and Conditioning

Published:2023-06-06 Issue:PLDI Volume:7 Page:1-24
ISSN:2475-1421
Container-title:Proceedings of the ACM on Programming Languages
language:en
Short-container-title:Proc. ACM Program. Lang.

Author:

Bagnall Alexander¹^ORCID,Stewart Gordon²^ORCID,Banerjee Anindya³^ORCID

Affiliation:

1. Ohio University, USA

2. Bedrock Systems, USA

3. IMDEA Software Institute, Spain

Abstract

We present Zar: a formally verified compiler pipeline from discrete probabilistic programs with unbounded loops in the conditional probabilistic guarded command language (cpGCL) to proved-correct executable samplers in the random bit model. We exploit the key idea that all discrete probability distributions can be reduced to unbiased coin-flipping schemes. The compiler pipeline first translates cpGCL programs into choice-fix trees, an intermediate representation suitable for reduction of biased probabilistic choices. Choice-fix trees are then translated to coinductive interaction trees for execution within the random bit model. The correctness of the composed translations establishes the sampling equidistribution theorem: compiled samplers are correct wrt. the conditional weakest pre-expectation semantics of cpGCL source programs. Zar is implemented and fully verified in the Coq proof assistant. We extract verified samplers to OCaml and Python and empirically validate them on a number of illustrative examples.

Publisher

Association for Computing Machinery (ACM)

Subject

Safety, Risk, Reliability and Quality,Software

Link

https://dl.acm.org/doi/pdf/10.1145/3591220

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