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We present Zar: a formally verified compiler pipeline from discreteprobabilistic programs with unbounded loops in the conditional probabilisticguarded command language (cpGCL) to proved-correct executable samplers in therandom bit model. We exploit the key idea that all discrete probabilitydistributions can be reduced to unbiased coin-flipping schemes. The compilerpipeline first translates a cpGCL program into choice-fix trees, anintermediate representation suitable for reduction of biased probabilisticchoices. Choice-fix trees are then translated to coinductive interaction treesfor execution within the random bit model. The correctness of the composedtranslations establishes the sampling equidistribution theorem: compiledsamplers are correct wrt. the conditional weakest pre-expectation semantics ofcpGCL source programs. Zar is implemented and fully verified in the Coq proofassistant. We extract verified samplers to OCaml and Python and empiricallyvalidate them on a number of illustrative examples.

Formally Verified Samplers From Probabilistic Programs With Loops and Conditioning