Verified Density Compilation for a Probabilistic Programming Language
summary
Provides a mechanized semantics for a Stan subset and verifies three density-compilation passes in Coq, producing ProbCompCert that connects to CompCert down to assembly. Proofs use forward simulation plus denotational reasoning to show transforms like reparameterization and additive-constant elimination preserve the posterior (up to normalization), and the effort uncovers an error in the Stan reference manual. Main limitation is that correctness is idealized over exact reals, not finite-precision floating-point.
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chapters (10)
- 0:00Introduction
- 1:07Project overview
- 3:17Density compilation in Stan
- 4:21Compiler specification
- 7:51Compiler correctness proof
- 9:56Reparameterization pass
- 12:25Additive constant optimization
- 14:33Floating point limits
- 15:57Conclusion
- 16:24Q&A
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