Newtonian Program Analysis of Probabilistic Programs
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917606961709056 |
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| author | Wang, Di Reps, Thomas |
| author_facet | Wang, Di Reps, Thomas |
| contents | Due to their quantitative nature, probabilistic programs pose non-trivial challenges for designing compositional and efficient program analyses. Many analyses for probabilistic programs rely on iterative approximation. This article presents an interprocedural dataflow-analysis framework, called NPA-PMA, for designing and implementing (partially) non-iterative program analyses of probabilistic programs with unstructured control-flow, nondeterminism, and general recursion. NPA-PMA is based on Newtonian Program Analysis (NPA), a generalization of Newton's method to solve equation systems over semirings. The key challenge for developing NPA-PMA is to handle multiple kinds of confluences in both the algebraic structures that specify analyses and the equation systems that encode control flow: semirings support a single confluence operation, whereas NPA-PMA involves three confluence operations (conditional, probabilistic, and nondeterministic).
Our work introduces $ω$-continuous pre-Markov algebras ($ω$PMAs) to factor out common parts of different analyses; adopts regular infinite-tree expressions to encode program-execution paths in control-flow hyper-graphs; and presents a linearization method that makes Newton's method applicable to the setting of regular-infinite-tree equations over $ω$PMAs. NPA-PMA allows analyses to supply a non-iterative strategy to solve linearized equations. Our experimental evaluation demonstrates that (i) NPA-PMA holds considerable promise for outperforming Kleene iteration, and (ii) provides great generality for designing program analyses. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_09064 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Newtonian Program Analysis of Probabilistic Programs Wang, Di Reps, Thomas Programming Languages Due to their quantitative nature, probabilistic programs pose non-trivial challenges for designing compositional and efficient program analyses. Many analyses for probabilistic programs rely on iterative approximation. This article presents an interprocedural dataflow-analysis framework, called NPA-PMA, for designing and implementing (partially) non-iterative program analyses of probabilistic programs with unstructured control-flow, nondeterminism, and general recursion. NPA-PMA is based on Newtonian Program Analysis (NPA), a generalization of Newton's method to solve equation systems over semirings. The key challenge for developing NPA-PMA is to handle multiple kinds of confluences in both the algebraic structures that specify analyses and the equation systems that encode control flow: semirings support a single confluence operation, whereas NPA-PMA involves three confluence operations (conditional, probabilistic, and nondeterministic). Our work introduces $ω$-continuous pre-Markov algebras ($ω$PMAs) to factor out common parts of different analyses; adopts regular infinite-tree expressions to encode program-execution paths in control-flow hyper-graphs; and presents a linearization method that makes Newton's method applicable to the setting of regular-infinite-tree equations over $ω$PMAs. NPA-PMA allows analyses to supply a non-iterative strategy to solve linearized equations. Our experimental evaluation demonstrates that (i) NPA-PMA holds considerable promise for outperforming Kleene iteration, and (ii) provides great generality for designing program analyses. |
| title | Newtonian Program Analysis of Probabilistic Programs |
| topic | Programming Languages |
| url | https://arxiv.org/abs/2307.09064 |