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Asynchronous Probabilistic Couplings in Higher-Order Separation Logic

Authors:

Simon Oddershede Gregersen,

Alejandro Aguirre,

Philipp G. Haselwarter,

Joseph Tassarotti,

Lars BirkedalAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 8, Issue POPL

Article No.: 26, Pages 753 - 784

https://doi.org/10.1145/3632868

Published: 05 January 2024 Publication History

Abstract

Probabilistic couplings are the foundation for many probabilistic relational program logics and arise when relating random sampling statements across two programs. In relational program logics, this manifests as dedicated coupling rules that, e.g., say we may reason as if two sampling statements return the same value. However, this approach fundamentally requires aligning or "synchronizing" the sampling statements of the two programs which is not always possible.

In this paper, we develop Clutch, a higher-order probabilistic relational separation logic that addresses this issue by supporting asynchronous probabilistic couplings. We use Clutch to develop a logical step-indexed logical relation to reason about contextual refinement and equivalence of higher-order programs written in a rich language with a probabilistic choice operator, higher-order local state, and impredicative polymorphism. Finally, we demonstrate our approach on a number of case studies.

All the results that appear in the paper have been formalized in the Coq proof assistant using the Coquelicot library and the Iris separation logic framework.

References

[1]

Martín Abadi and Leslie Lamport. 1988. The Existence of Refinement Mappings. In Proceedings of the Third Annual Symposium on Logic in Computer Science (LICS ’88), Edinburgh, Scotland, UK, July 5-8, 1988. 165–175. https://doi.org/10.1109/LICS.1988.5115

[2]

Martín Abadi and Leslie Lamport. 1991. The Existence of Refinement Mappings. Theor. Comput. Sci., 82, 2 (1991), 253–284. https://doi.org/10.1016/0304-3975(91)90224-P

[3]

Carmine Abate, Philipp G. Haselwarter, Exequiel Rivas, Antoine Van Muylder, Théo Winterhalter, Catalin Hritcu, Kenji Maillard, and Bas Spitters. 2021. SSProve: A Foundational Framework for Modular Cryptographic Proofs in Coq. In 34th IEEE Computer Security Foundations Symposium, CSF 2021, Dubrovnik, Croatia, June 21-25, 2021. 1–15. https://doi.org/10.1109/CSF51468.2021.00048

[4]

Alejandro Aguirre, Gilles Barthe, Lars Birkedal, Ales Bizjak, Marco Gaboardi, and Deepak Garg. 2018. Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus. In Programming Languages and Systems - 27th European Symposium on Programming, ESOP 2018, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018, Thessaloniki, Greece, April 14-20, 2018, Proceedings. 214–241. https://doi.org/10.1007/978-3-319-89884-1_8

[5]

Alejandro Aguirre, Gilles Barthe, Marco Gaboardi, Deepak Garg, Shin-ya Katsumata, and Tetsuya Sato. 2021. Higher-order probabilistic adversarial computations: categorical semantics and program logics. Proc. ACM Program. Lang., 5, ICFP (2021), 1–30. https://doi.org/10.1145/3473598

[6]

David J. Aldous. 1983. Random walks on finite groups and rapidly mixing Markov chains. Séminaire de probabilités de Strasbourg, 17 (1983), 243–297. http://www.numdam.org/item/SPS_1983__17__243_0/

[7]

José Bacelar Almeida, Cécile Baritel-Ruet, Manuel Barbosa, Gilles Barthe, François Dupressoir, Benjamin Grégoire, Vincent Laporte, Tiago Oliveira, Alley Stoughton, and Pierre-Yves Strub. 2019. Machine-Checked Proofs for Cryptographic Standards: Indifferentiability of Sponge and Secure High-Assurance Implementations of SHA-3. In Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, CCS 2019, London, UK, November 11-15, 2019, Lorenzo Cavallaro, Johannes Kinder, XiaoFeng Wang, and Jonathan Katz (Eds.). ACM, 1607–1622. https://doi.org/10.1145/3319535.3363211

[8]

Andrew W. Appel. 2001. Foundational Proof-Carrying Code. In 16th Annual IEEE Symposium on Logic in Computer Science, Boston, Massachusetts, USA, June 16-19, 2001, Proceedings. 247–256. https://doi.org/10.1109/LICS.2001.932501

[9]

Jialu Bao, Simon Docherty, Justin Hsu, and Alexandra Silva. 2021. A Bunched Logic for Conditional Independence. In 36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021, Rome, Italy, June 29 - July 2, 2021. IEEE, 1–14. https://doi.org/10.1109/LICS52264.2021.9470712

[10]

Jialu Bao, Marco Gaboardi, Justin Hsu, and Joseph Tassarotti. 2022. A separation logic for negative dependence. Proc. ACM Program. Lang., 6, POPL (2022), 1–29. https://doi.org/10.1145/3498719

[11]

Manuel Barbosa, Gilles Barthe, Benjamin Grégoire, Adrien Koutsos, and Pierre-Yves Strub. 2021. Mechanized Proofs of Adversarial Complexity and Application to Universal Composability. In CCS ’21: 2021 ACM SIGSAC Conference on Computer and Communications Security, Virtual Event, Republic of Korea, November 15 - 19, 2021, Yongdae Kim, Jong Kim, Giovanni Vigna, and Elaine Shi (Eds.). ACM, 2541–2563. https://doi.org/10.1145/3460120.3484548

[12]

Elaine B. Barker and John M. Kelsey. 2015. Recommendation for Random Number Generation Using Deterministic Random Bit Generators. National Institute of Standards and Technology. https://doi.org/10.6028/nist.sp.800-90ar1

[13]

Gilles Barthe, François Dupressoir, Benjamin Grégoire, César Kunz, Benedikt Schmidt, and Pierre-Yves Strub. 2013. EasyCrypt: A Tutorial. In Foundations of Security Analysis and Design VII - FOSAD 2012/2013 Tutorial Lectures. 146–166. https://doi.org/10.1007/978-3-319-10082-1_6

[14]

Gilles Barthe, Thomas Espitau, Benjamin Grégoire, Justin Hsu, Léo Stefanesco, and Pierre-Yves Strub. 2015. Relational Reasoning via Probabilistic Coupling. In Logic for Programming, Artificial Intelligence, and Reasoning - 20th International Conference, LPAR-20 2015, Suva, Fiji, November 24-28, 2015, Proceedings. 387–401. https://doi.org/10.1007/978-3-662-48899-7_27

[15]

Gilles Barthe, Thomas Espitau, Benjamin Grégoire, Justin Hsu, and Pierre-Yves Strub. 2018. Proving expected sensitivity of probabilistic programs. Proc. ACM Program. Lang., 2, POPL (2018), 57:1–57:29. https://doi.org/10.1145/3158145

[16]

Gilles Barthe, Noémie Fong, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, and Pierre-Yves Strub. 2016. Advanced Probabilistic Couplings for Differential Privacy. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, Vienna, Austria, October 24-28, 2016, Edgar R. Weippl, Stefan Katzenbeisser, Christopher Kruegel, Andrew C. Myers, and Shai Halevi (Eds.). ACM, 55–67. https://doi.org/10.1145/2976749.2978391

[17]

Gilles Barthe, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, and Pierre-Yves Strub. 2016. Proving Differential Privacy via Probabilistic Couplings. In Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS ’16, New York, NY, USA, July 5-8, 2016. 749–758. https://doi.org/10.1145/2933575.2934554

[18]

Gilles Barthe, Benjamin Grégoire, and Santiago Zanella Béguelin. 2009. Formal certification of code-based cryptographic proofs. In Proceedings of the 36th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2009, Savannah, GA, USA, January 21-23, 2009. 90–101. https://doi.org/10.1145/1480881.1480894

[19]

Gilles Barthe, Benjamin Grégoire, and Santiago Zanella Béguelin. 2010. Programming Language Techniques for Cryptographic Proofs. In Interactive Theorem Proving, First International Conference, ITP 2010, Edinburgh, UK, July 11-14, 2010. Proceedings. 115–130. https://doi.org/10.1007/978-3-642-14052-5_10

[20]

Gilles Barthe, Justin Hsu, and Kevin Liao. 2020. A probabilistic separation logic. Proc. ACM Program. Lang., 4, POPL (2020), 55:1–55:30. https://doi.org/10.1145/3371123

[21]

Gilles Barthe, Boris Köpf, Federico Olmedo, and Santiago Zanella Béguelin. 2012. Probabilistic relational reasoning for differential privacy. In Proceedings of the 39th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2012, Philadelphia, Pennsylvania, USA, January 22-28, 2012. 97–110. https://doi.org/10.1145/2103656.2103670

[22]

Kevin Batz, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, and Thomas Noll. 2019. Quantitative separation logic: a logic for reasoning about probabilistic pointer programs. Proc. ACM Program. Lang., 3, POPL (2019), 34:1–34:29. https://doi.org/10.1145/3290347

[23]

Mihir Bellare and Phillip Rogaway. 1993. Random Oracles are Practical: A Paradigm for Designing Efficient Protocols. In CCS ’93, Proceedings of the 1st ACM Conference on Computer and Communications Security, Fairfax, Virginia, USA, November 3-5, 1993. 62–73. https://doi.org/10.1145/168588.168596

[24]

Mihir Bellare and Phillip Rogaway. 2004. Code-Based Game-Playing Proofs and the Security of Triple Encryption. Cryptology ePrint Archive, Paper 2004/331. https://eprint.iacr.org/2004/331

[25]

Mihir Bellare and Phillip Rogaway. 2006. The Security of Triple Encryption and a Framework for Code-Based Game-Playing Proofs. In Advances in Cryptology - EUROCRYPT 2006, Serge Vaudenay (Ed.). 409–426.

[26]

Aleš Bizjak. 2016. On Semantics and Applications of Guarded Recursion. Ph. D. Dissertation. Aarhus University.

[27]

Ales Bizjak and Lars Birkedal. 2015. Step-Indexed Logical Relations for Probability. In Foundations of Software Science and Computation Structures - 18th International Conference, FoSSaCS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015. Proceedings. 279–294. https://doi.org/10.1007/978-3-662-46678-0_18

[28]

Sylvie Boldo, Catherine Lelay, and Guillaume Melquiond. 2015. Coquelicot: A User-Friendly Library of Real Analysis for Coq. Math. Comput. Sci., 9, 1 (2015), 41–62.

[29]

Olivier Bousquet and André Elisseeff. 2002. Stability and Generalization. J. Mach. Learn. Res., 2 (2002), mar, 499–526. issn:1532-4435 https://doi.org/10.1162/153244302760200704

[30]

Tej Chajed, Joseph Tassarotti, M. Frans Kaashoek, and Nickolai Zeldovich. 2019. Verifying concurrent, crash-safe systems with Perennial. In Proceedings of the 27th ACM Symposium on Operating Systems Principles, SOSP 2019, Huntsville, ON, Canada, October 27-30, 2019. 243–258. https://doi.org/10.1145/3341301.3359632

[31]

Ugo Dal Lago and Francesco Gavazzo. 2021. Differential logical relations, part II increments and derivatives. Theor. Comput. Sci., 895 (2021), 34–47. https://doi.org/10.1016/j.tcs.2021.09.027

[32]

Ugo Dal Lago and Francesco Gavazzo. 2022. Effectful program distancing. Proc. ACM Program. Lang., 6, POPL (2022), 1–30. https://doi.org/10.1145/3498680

[33]

Derek Dreyer, Amal Ahmed, and Lars Birkedal. 2011. Logical Step-Indexed Logical Relations. Log. Methods Comput. Sci., 7, 2 (2011), https://doi.org/10.2168/LMCS-7(2:16)2011

[34]

Derek Dreyer, Georg Neis, and Lars Birkedal. 2012. The impact of higher-order state and control effects on local relational reasoning. J. Funct. Program., 22, 4-5 (2012), 477–528. https://doi.org/10.1017/S095679681200024X

[35]

Cynthia Dwork and Aaron Roth. 2013. The Algorithmic Foundations of Differential Privacy. Foundations and Trends® in Theoretical Computer Science, 9, 3-4 (2013), 211–407. issn:1551-305X, 1551-3068 https://doi.org/10.1561/0400000042

[36]

Taher Elgamal. 1985. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory, 31, 4 (1985), 469–472. https://doi.org/10.1109/TIT.1985.1057074

[37]

Dan Frumin, Robbert Krebbers, and Lars Birkedal. 2021. Compositional Non-Interference for Fine-Grained Concurrent Programs. In 42nd IEEE Symposium on Security and Privacy, SP 2021, San Francisco, CA, USA, 24-27 May 2021. 1416–1433. https://doi.org/10.1109/SP40001.2021.00003

[38]

Dan Frumin, Robbert Krebbers, and Lars Birkedal. 2021. ReLoC Reloaded: A Mechanized Relational Logic for Fine-Grained Concurrency and Logical Atomicity. Log. Methods Comput. Sci., 17, 3 (2021), https://doi.org/10.46298/lmcs-17(3:9)2021

[39]

Lennard Gäher, Michael Sammler, Simon Spies, Ralf Jung, Hoang-Hai Dang, Robbert Krebbers, Jeehoon Kang, and Derek Dreyer. 2022. Simuliris: a separation logic framework for verifying concurrent program optimizations. Proc. ACM Program. Lang., 6, POPL (2022), 1–31. https://doi.org/10.1145/3498689

[40]

Joshua Gancher, Kristina Sojakova, Xiong Fan, Elaine Shi, and Greg Morrisett. 2023. A Core Calculus for Equational Proofs of Cryptographic Protocols. Proc. ACM Program. Lang., 7, POPL (2023), Article 30, jan, 27 pages. https://doi.org/10.1145/3571223

[41]

Aïna Linn Georges, Alix Trieu, and Lars Birkedal. 2022. Le temps des cerises: efficient temporal stack safety on capability machines using directed capabilities. Proc. ACM Program. Lang., 6, OOPSLA1 (2022), 1–30. https://doi.org/10.1145/3527318

[42]

Shafi Goldwasser and Silvio Micali. 1984. Probabilistic Encryption. J. Comput. Syst. Sci., 28, 2 (1984), 270–299. https://doi.org/10.1016/0022-0000(84)90070-9

[43]

Simon Oddershede Gregersen, Alejandro Aguirre, Philipp G. Haselwarter, Joseph Tassarotti, and Lars Birkedal. 2023. Asynchronous Probabilistic Couplings in Higher- Order Separation Logic - Coq Artifact. https://doi.org/10.5281/zenodo.8424490

[44]

Simon Oddershede Gregersen, Alejandro Aguirre, Philipp G. Haselwarter, Joseph Tassarotti, and Lars Birkedal. 2023. Asynchronous Probabilistic Couplings in Higher-Order Separation Logic. CoRR, abs/2301.10061 (2023), https://doi.org/10.48550/ARXIV.2301.10061 arXiv:2301.10061.

[45]

Simon Oddershede Gregersen, Johan Bay, Amin Timany, and Lars Birkedal. 2021. Mechanized logical relations for termination-insensitive noninterference. Proc. ACM Program. Lang., 5, POPL (2021), 1–29. https://doi.org/10.1145/3434291

[46]

Philipp G. Haselwarter, Exequiel Rivas, Antoine Van Muylder, Théo Winterhalter, Carmine Abate, Nikolaj Sidorenco, Catalin Hritcu, Kenji Maillard, and Bas Spitters. 2021. SSProve: A Foundational Framework for Modular Cryptographic Proofs in Coq. Cryptology ePrint Archive, Paper 2021/397. https://eprint.iacr.org/2021/397

[47]

Patricia Johann, Alex Simpson, and Janis Voigtländer. 2010. A Generic Operational Metatheory for Algebraic Effects. In Proceedings of the 25th Annual IEEE Symposium on Logic in Computer Science, LICS 2010, 11-14 July 2010, Edinburgh, United Kingdom. 209–218. https://doi.org/10.1109/LICS.2010.29

[48]

Ralf Jung, Robbert Krebbers, Lars Birkedal, and Derek Dreyer. 2016. Higher-order ghost state. In Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming, ICFP 2016, Nara, Japan, September 18-22, 2016. 256–269. https://doi.org/10.1145/2951913.2951943

[49]

Ralf Jung, Robbert Krebbers, Jacques-Henri Jourdan, Ales Bizjak, Lars Birkedal, and Derek Dreyer. 2018. Iris from the ground up: A modular foundation for higher-order concurrent separation logic. J. Funct. Program., 28 (2018), e20. https://doi.org/10.1017/S0956796818000151

[50]

Ralf Jung, Rodolphe Lepigre, Gaurav Parthasarathy, Marianna Rapoport, Amin Timany, Derek Dreyer, and Bart Jacobs. 2020. The future is ours: prophecy variables in separation logic. Proc. ACM Program. Lang., 4, POPL (2020), 45:1–45:32. https://doi.org/10.1145/3371113

[51]

Ralf Jung, David Swasey, Filip Sieczkowski, Kasper Svendsen, Aaron Turon, Lars Birkedal, and Derek Dreyer. 2015. Iris: Monoids and Invariants as an Orthogonal Basis for Concurrent Reasoning. In Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2015, Mumbai, India, January 15-17, 2015. 637–650. https://doi.org/10.1145/2676726.2676980

[52]

Robbert Krebbers, Ralf Jung, Ales Bizjak, Jacques-Henri Jourdan, Derek Dreyer, and Lars Birkedal. 2017. The Essence of Higher-Order Concurrent Separation Logic. In Programming Languages and Systems - 26th European Symposium on Programming, ESOP 2017, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Uppsala, Sweden, April 22-29, 2017, Proceedings. 696–723. https://doi.org/10.1007/978-3-662-54434-1_26

[53]

Robbert Krebbers, Amin Timany, and Lars Birkedal. 2017. Interactive proofs in higher-order concurrent separation logic. In Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages, POPL 2017, Paris, France, January 18-20, 2017. 205–217. https://doi.org/10.1145/3009837.3009855

[54]

T. Lindvall. 2002. Lectures on the Coupling Method. Dover Publications, Incorporated. isbn:978-0-486-42145-2 lccn:92012811

[55]

Arno Mittelbach and Marc Fischlin. 2021. The Theory of Hash Functions and Random Oracles - An Approach to Modern Cryptography. Springer. isbn:978-3-030-63286-1 https://doi.org/10.1007/978-3-030-63287-8

[56]

Adam Petcher and Greg Morrisett. 2015. The Foundational Cryptography Framework. In Principles of Security and Trust - 4th International Conference, POST 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings. 53–72. https://doi.org/10.1007/978-3-662-46666-7_4

[57]

Andrew M. Pitts and Ian D. B. Stark. 1998. Operational Reasoning for Functions with Local State. In Higher Order Operational Techniques in Semantics, A. D. Gordon and A. M. Pitts (Eds.). Cambridge University Press, 227–273.

[58]

Mike Rosulek. 2020. The Joy of Cryptography. http://web.engr.oregonstate.edu/~rosulekm/crypto/

[59]

Davide Sangiorgi and Valeria Vignudelli. 2016. Environmental bisimulations for probabilistic higher-order languages. In Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2016, St. Petersburg, FL, USA, January 20 - 22, 2016. 595–607. https://doi.org/10.1145/2837614.2837651

[60]

Raimund Seidel and Cecilia R. Aragon. 1996. Randomized Search Trees. Algorithmica, 16, 4/5 (1996), 464–497. https://doi.org/10.1007/BF01940876

[61]

Kasper Svendsen and Lars Birkedal. 2014. Impredicative Concurrent Abstract Predicates. In Programming Languages and Systems - 23rd European Symposium on Programming, ESOP 2014, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014, Grenoble, France, April 5-13, 2014, Proceedings. 149–168. https://doi.org/10.1007/978-3-642-54833-8_9

[62]

Joseph Tassarotti and Robert Harper. 2019. A separation logic for concurrent randomized programs. Proc. ACM Program. Lang., 3, POPL (2019), 64:1–64:30. https://doi.org/10.1145/3290377

[63]

The Coq Development Team. 2022. The Coq Proof Assistant. https://doi.org/10.5281/zenodo.7313584

[64]

The Iris Development Team. 2022. The Iris 4.0 Reference. https://plv.mpi-sws.org/iris/appendix-4.0.pdf

[65]

Hermann Thorisson. 2000. Coupling, stationarity, and regeneration. Springer-Verlag, New York. isbn:0-387-98779-7

[66]

Amin Timany and Lars Birkedal. 2019. Mechanized relational verification of concurrent programs with continuations. Proc. ACM Program. Lang., 3, ICFP (2019), 105:1–105:28. https://doi.org/10.1145/3341709

[67]

Amin Timany, Simon Oddershede Gregersen, Léo Stefanesco, Léon Gondelman, Abel Nieto, and Lars Birkedal. 2021. Trillium: Unifying Refinement and Higher-Order Distributed Separation Logic. CoRR, abs/2109.07863 (2021), arXiv:2109.07863. arxiv:2109.07863

[68]

Amin Timany, Robbert Krebbers, Derek Dreyer, and Lars Birkedal. 2022. A Logical Approach to Type Soundness. https://iris-project.org/pdfs/2022-submitted-logical-type-soundness.pdf Unpublished manuscript

[69]

Amin Timany, Léo Stefanesco, Morten Krogh-Jespersen, and Lars Birkedal. 2018. A logical relation for monadic encapsulation of state: proving contextual equivalences in the presence of runST. Proc. ACM Program. Lang., 2, POPL (2018), 64:1–64:28. https://doi.org/10.1145/3158152

[70]

Aaron Turon, Derek Dreyer, and Lars Birkedal. 2013. Unifying refinement and hoare-style reasoning in a logic for higher-order concurrency. In ACM SIGPLAN International Conference on Functional Programming, ICFP’13, Boston, MA, USA - September 25 - 27, 2013. 377–390. https://doi.org/10.1145/2500365.2500600

[71]

Aaron Joseph Turon, Jacob Thamsborg, Amal Ahmed, Lars Birkedal, and Derek Dreyer. 2013. Logical relations for fine-grained concurrency. In The 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL ’13, Rome, Italy - January 23 - 25, 2013. 343–356. https://doi.org/10.1145/2429069.2429111

[72]

C. Villani. 2008. Optimal Transport: Old and New. Springer Berlin Heidelberg. isbn:9783540710509 lccn:2008932183

[73]

Mitchell Wand, Ryan Culpepper, Theophilos Giannakopoulos, and Andrew Cobb. 2018. Contextual equivalence for a probabilistic language with continuous random variables and recursion. Proc. ACM Program. Lang., 2, ICFP (2018), 87:1–87:30. https://doi.org/10.1145/3236782

[74]

Yizhou Zhang and Nada Amin. 2022. Reasoning about "reasoning about reasoning": semantics and contextual equivalence for probabilistic programs with nested queries and recursion. Proc. ACM Program. Lang., 6, POPL (2022), 1–28. https://doi.org/10.1145/3498677

Cited By

Haselwarter PLi Kde Medeiros MGregersen SAguirre ATassarotti JBirkedal L(2024)Tachis: Higher-Order Separation Logic with Credits for Expected CostsProceedings of the ACM on Programming Languages10.1145/36897538:OOPSLA2(1189-1218)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689753
Aguirre AHaselwarter Pde Medeiros MLi KGregersen STassarotti JBirkedal L(2024)Error Credits: Resourceful Reasoning about Error Bounds for Higher-Order Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/36746358:ICFP(284-316)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674635
Gregersen SAguirre AHaselwarter PTassarotti JBirkedal L(2024)Almost-Sure Termination by Guarded RefinementProceedings of the ACM on Programming Languages10.1145/36746328:ICFP(203-233)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674632

Index Terms

Asynchronous Probabilistic Couplings in Higher-Order Separation Logic
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic algorithms
2. Theory of computation

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 8, Issue POPL

January 2024

2820 pages

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DOI:10.1145/3554315

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Cited By

Haselwarter PLi Kde Medeiros MGregersen SAguirre ATassarotti JBirkedal L(2024)Tachis: Higher-Order Separation Logic with Credits for Expected CostsProceedings of the ACM on Programming Languages10.1145/36897538:OOPSLA2(1189-1218)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689753
Aguirre AHaselwarter Pde Medeiros MLi KGregersen STassarotti JBirkedal L(2024)Error Credits: Resourceful Reasoning about Error Bounds for Higher-Order Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/36746358:ICFP(284-316)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674635
Gregersen SAguirre AHaselwarter PTassarotti JBirkedal L(2024)Almost-Sure Termination by Guarded RefinementProceedings of the ACM on Programming Languages10.1145/36746328:ICFP(203-233)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674632

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