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Trace types and denotational semantics for sound programmable inference in probabilistic languages

Alexander K. Lew, Marco F. Cusumano-Towner, Benjamin Sherman, Michael Carbin, Vikash K. Mansinghka
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
We are grateful to the referees for their thoughtful and constructive input, and also to Hengchu Zhang, Jonathan Rees, Cameron Freer, Eric Atkinson, Feras Saad, and Ben Zinberg for useful discussions and  ...  ACKNOWLEDGMENTS This material is based upon work supported by philanthropic gifts from the Siegel Family Foundation and from the Aphorism Foundation, and also by a research contract from the Intel Probabilistic  ...  . 2 * y) ( Sound Programmable Inference With trace types in hand, we can formulate sound-by-construction versions of a variety of programmable inference constructs.  ... 
doi:10.1145/3371087 fatcat:kf4vfvzt7rdvzencdtksbk3moq

Sound Probabilistic Inference via Guide Types [article]

Di Wang, Jan Hoffmann, Thomas Reps
2021 arXiv   pre-print
Probabilistic programming languages aim to describe and automate Bayesian modeling and inference.  ...  For Bayesian inference to be sound, guide programs must be compatible with model programs.  ...  In this paper, we focus on a trace-based scheme for programmable inference.  ... 
arXiv:2104.03598v1 fatcat:vpobeqiwhnb5bbvaxpicwzvyle

Towards Denotational Semantics of AD for Higher-Order, Recursive, Probabilistic Languages [article]

Alexander K. Lew, Mathieu Huot, Vikash K. Mansinghka
2021 arXiv   pre-print
We also apply the framework to study probabilistic programs, and recover a recent result from Mak et al. [2021] via a novel denotational argument.  ...  Our main result is that even in this general setting, a version of Lee et al. [2020]'s correctness theorem (originally proven for a first-order language without partiality or recursion) holds: all programs  ...  Marco F Cusumano-Towner, Feras A Saad, Alexander K Lew, and Vikash K Mansinghka. Gen: a general-purpose probabilistic programming system with programmable inference.  ... 
arXiv:2111.15456v2 fatcat:3nhzpfr5u5cstonw7slwrz7co4

Running Probabilistic Programs Backwards [article]

Neil Toronto and Jay McCarthy and David Van Horn
2015 arXiv   pre-print
We implement the abstract semantics and use the implementation to carry out Bayesian inference, stochastic ray tracing (a rare event simulation), and probabilistic verification of floating-point error  ...  Many probabilistic programming languages allow programs to be run under constraints in order to carry out Bayesian inference.  ...  Special thanks to Mitchell Wand for careful review and helpful feedback.  ... 
arXiv:1412.4053v2 fatcat:ewitbymf4nfq7p2pgztehrjkli

Semantics for probabilistic programming

Sam Staton, Hongseok Yang, Frank Wood, Chris Heunen, Ohad Kammar
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
We define a metalanguage (an idealised version of Anglican) for probabilistic computation with the above features, develop both operational and denotational semantics, and prove soundness, adequacy, and  ...  We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture  ...  Moreover, such languages come with generic inference algorithms, relieving the programmer of the nontrivial task of (algorithmically) answering queries about her probabilistic models.  ... 
doi:10.1145/2933575.2935313 dblp:conf/lics/StatonYWHK16 fatcat:ggvgmheyang6ffdofh3civco2a

Abstract Interpretation Based Formal Methods and Future Challenges [chapter]

Patrick Cousot
2001 Lecture Notes in Computer Science  
In the second part of the paper, we compare static program analysis with deductive methods, model-checking and type inference.  ...  We illustrate informally the application of abstraction to the semantics of programming languages as well as to static program analysis.  ...  Acknowledgements I thank Radhia Cousot and Reinhard Wilhelm for their comments on a preliminary version of this paper. This work was supported by the daedalus (58) and tuamotu (59) projects.  ... 
doi:10.1007/3-540-44577-3_10 fatcat:5d6txyozgfclpidmpgia2uqvla

Enforcing Ideal-World Leakage Bounds in Real-World Secret Sharing MPC Frameworks

Jose Bacelar Almeida, Manuel Barbosa, Gilles Barthe, Hugo Pacheco, Vitor Pereira, Bernardo Portela
2018 2018 IEEE 31st Computer Security Foundations Symposium (CSF)  
We give a language-based security treatment of domain-specific languages and compilers for secure multi-party computation, a cryptographic paradigm that enables collaborative computation over encrypted  ...  Computations are specified in a core imperative language, as if they were intended to be executed by a trusted-third party, and formally verified against an information-flow policy modelling (an upper  ...  Figure 4 : 4 Type system of our source language. Figure 5 : 5 Inference system for Security Hoare Logic. V.  ... 
doi:10.1109/csf.2018.00017 dblp:conf/csfw/AlmeidaBB0PP18 fatcat:ek4sejy3brfn7b34j3ozvowk44

Raising Expectations: Automating Expected Cost Analysis with Types [article]

Di Wang, David M Kahn, Jan Hoffmann
2020 arXiv   pre-print
This article presents a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs.  ...  Bound inference is enabled by local type rules that reduce type inference to linear constraint solving.  ...  [Lew et al. 2020] have developed a type system for programmable probabilistic inference with trace types, where well-typed inference programs soundly derive posterior distributions by construction.  ... 
arXiv:2006.14010v2 fatcat:vi5l7ycbnzcvlj2eqykrlm6akm

Building verification condition generators by compositional extensions

I.S.W.B. Prasetya, A.A. Fakultas, T.E.J. Vos, A. van Leeuwen
2005 Third IEEE International Conference on Software Engineering and Formal Methods (SEFM'05)  
We show that using our technique the extension can be implemented in a simple and compositional way, without any change to the underlying logic.  ...  Moreover, it enables us to add an ability to generate validation traces.  ...  For example, the inference rule that handles assignments in java-like OO languages is quite complicated [7, 18] and users would definitely benefit from a trace that can, for example, be sent to a third  ... 
doi:10.1109/sefm.2005.11 dblp:conf/sefm/PrasetyaAVL05 fatcat:bvxo23rfnzbmbnuejqd7pfhy4q

A probabilistic language based on sampling functions

Sungwoo Park, Frank Pfenning, Sebastian Thrun
2008 ACM Transactions on Programming Languages and Systems  
As such, λ enables programmers to formally express and reason about sampling methods developed in simulation theory.  ...  Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power.  ...  Proposition 7.1 proves the soundness of the translation: a well-typed term or expression in the source language is translated into a well-typed expression in the target language.  ... 
doi:10.1145/1452044.1452048 fatcat:bfbgi2fvyjdq7iceh7eeudf7ay

A probabilistic language based upon sampling functions

Sungwoo Park, Frank Pfenning, Sebastian Thrun
2005 Proceedings of the 32nd ACM SIGPLAN-SIGACT sysposium on Principles of programming languages - POPL '05  
As such, λ enables programmers to formally express and reason about sampling methods developed in simulation theory.  ...  Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power.  ...  In the case of λ , terms denote regular values and expressions denote probabilistic computations in the sense that under its operational semantics, a term reduces to a unique regular value and an expression  ... 
doi:10.1145/1040305.1040320 dblp:conf/popl/ParkPT05 fatcat:wv454xzgjnbrddhqurggzn76d4

A probabilistic language based upon sampling functions

Sungwoo Park, Frank Pfenning, Sebastian Thrun
2005 SIGPLAN notices  
As such, λ enables programmers to formally express and reason about sampling methods developed in simulation theory.  ...  Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power.  ...  In the case of λ , terms denote regular values and expressions denote probabilistic computations in the sense that under its operational semantics, a term reduces to a unique regular value and an expression  ... 
doi:10.1145/1047659.1040320 fatcat:ch7f6355abcyrcoyfukiiydkre

Bayesian strategies: probabilistic programs as generalised graphical models [chapter]

Hugo Paquet
2021 Lecture Notes in Computer Science  
strategies provide a rich setting for denotational semantics.  ...  To demonstrate this we give a model for a general higher-order programming language with recursion, conditional statements, and primitives for sampling from continuous distributions and trace re-weighting  ...  For Metropolis-Hastings inference, Church [30] and Venture [41] manipulate dependency graphs for random variables ("computation traces" or "probabilistic execution traces"); Infer.NET [22] compiles  ... 
doi:10.1007/978-3-030-72019-3_19 fatcat:ssbcpqjgpbfrjiyo7kzxhddqom

CoALP-Ty'16 [article]

Ekaterina Komendantskaya, František Farka
2016 arXiv   pre-print
Clause Logic for Type Inference in Functional Languages and Beyond After discussion at the workshop authors of the extended abstracts will be invited to submit a full paper to go through a second round  ...  Grant Coalgebraic Logic Programming for Type Inference, by E.  ...  This in turn gives us a universe of discourse for exploring other semantics and proof systems for mixed inductive-coinductive logic programs.  ... 
arXiv:1612.03032v1 fatcat:d6gug5imufgwbcslntnyts4nim

Towards verified stochastic variational inference for probabilistic programs

Wonyeol Lee, Hangyeol Yu, Xavier Rival, Hongseok Yang
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
In this paper, we analyse one of the most fundamental and versatile variational inference algorithms, called score estimator or REINFORCE, using tools from denotational semantics and program analysis.  ...  Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines.  ...  In particular, addressing the later limitation might require techniques developed for proving that probabilistic systems has finite expected execution time.  ... 
doi:10.1145/3371084 fatcat:bta3gzcw5vcinn3u6th7jaeq5y
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