Cited By
View all- 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
Trillium: Higher-Order Concurrent and Distributed Separation Logic for Intensional Refinement
Authors: 
Amin Timany, 
Simon Oddershede Gregersen, 
Léo Stefanesco, Jonas Kastberg Hinrichsen, Léon Gondelman, Abel Nieto, Lars BirkedalAuthors Info & Claims
Amin Timany, Simon Oddershede Gregersen, Léo Stefanesco, Jonas Kastberg Hinrichsen, Léon Gondelman, Abel Nieto, Lars BirkedalAuthors Info & ClaimsArticle No.: 9, Pages 241 - 272
Abstract
Expressive state-of-the-art separation logics rely on step-indexing to model semantically complex features and to support modular reasoning about imperative higher-order concurrent and distributed programs. Step- indexing comes, however, with an inherent cost: it restricts the adequacy theorem of program logics to a fairly simple class of safety properties. In this paper, we explore if and how intensional refinement is a viable methodology for strengthening higher-order concurrent (and distributed) separation logic to prove non-trivial safety and liveness properties. Specifically, we introduce Trillium, a language-agnostic separation logic framework for showing intensional refinement relations between traces of a program and a model. We instantiate Trillium with a concurrent language and develop Fairis, a concurrent separation logic, that we use to show liveness properties of concurrent programs under fair scheduling assumptions through a fair liveness-preserving refinement of a model. We also instantiate Trillium with a distributed language and obtain an extension of Aneris, a distributed separation logic, which we use to show refinement relations between distributed systems and TLA+ models.
References
[1]
Lars Birkedal, Thomas Dinsdale-Young, Armaël Guéneau, Guilhem Jaber, Kasper Svendsen, and Nikos Tzevelekos. 2021. Theorems for Free from Separation Logic Specifications. Proc. ACM Program. Lang., 5, ICFP (2021), Article 81, aug, 29 pages. https://doi.org/10.1145/3473586
[2]
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
[3]
Saksham Chand, Yanhong A. Liu, and Scott D. Stoller. 2016. Formal Verification of Multi-Paxos for Distributed Consensus. In FM 2016: Formal Methods - 21st International Symposium, Limassol, Cyprus, November 9-11, 2016, Proceedings, John S. Fitzgerald, Constance L. Heitmeyer, Stefania Gnesi, and Anna Philippou (Eds.) (Lecture Notes in Computer Science, Vol. 9995). 119–136. https://doi.org/10.1007/978-3-319-48989-6_8
[4]
Rance Cleaveland and Oleg Sokolsky. 2001. CHAPTER 6 - Equivalence and Preorder Checking for Finite-State Systems. In Handbook of Process Algebra, J.A. Bergstra, A. Ponse, and S.A. Smolka (Eds.). Elsevier Science, Amsterdam. 391–424. isbn:978-0-444-82830-9 https://doi.org/10.1016/B978-044482830-9/50024-2
[5]
Dan Frumin, Robbert Krebbers, and Lars Birkedal. 2018. ReLoC: A Mechanised Relational Logic for Fine-Grained Concurrency. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018, Oxford, UK, July 09-12, 2018. 442–451. https://doi.org/10.1145/3209108.3209174
[6]
Dan Frumin, Robbert Krebbers, and Lars Birkedal. 2020. ReLoC Reloaded: A Mechanized Relational Logic for Fine-Grained Concurrency and Logical Atomicity. Log. Methods Comput. Sci., 17 (2020).
[7]
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
[8]
Álvaro García-Pérez, Alexey Gotsman, Yuri Meshman, and Ilya Sergey. 2018. Paxos Consensus, Deconstructed and Abstracted. 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, Amal Ahmed (Ed.) (Lecture Notes in Computer Science, Vol. 10801). Springer, 912–939. https://doi.org/10.1007/978-3-319-89884-1_32
[9]
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), Article 74, apr, 30 pages. https://doi.org/10.1145/3527318
[10]
Jim Gray. 1978. Notes on Data Base Operating Systems. In Operating Systems, An Advanced Course, Michael J. Flynn, Jim Gray, Anita K. Jones, Klaus Lagally, Holger Opderbeck, Gerald J. Popek, Brian Randell, Jerome H. Saltzer, and Hans-Rüdiger Wiehle (Eds.) (Lecture Notes in Computer Science, Vol. 60). Springer, 393–481. https://doi.org/10.1007/3-540-08755-9_9
[11]
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.
[12]
Ronghui Gu, Jérémie Koenig, Tahina Ramananandro, Zhong Shao, Xiongnan (Newman) Wu, Shu-Chun Weng, Haozhong Zhang, and Yu Guo. 2015. Deep Specifications and Certified Abstraction Layers. In POPL. ACM.
[13]
Ronghui Gu, Zhong Shao, Hao Chen, Xiongnan Wu, Jieung Kim, Vilhelm Sjöberg, and David Costanzo. 2016. CertiKOS: An Extensible Architecture for Building Certified Concurrent OS Kernels. In Proceedings of the 12th USENIX Conference on Operating Systems Design and Implementation (OSDI’16). USENIX Association, USA. 653–669. isbn:9781931971331
[14]
Ronghui Gu, Zhong Shao, Jieung Kim, Xiongnan (Newman) Wu, Jérémie Koenig, Vilhelm Sjöberg, Hao Chen, David Costanzo, and Tahina Ramananandro. 2018. Certified concurrent abstraction layers. In PLDI. ACM, 646–661.
[15]
Chris Hawblitzel, Jon Howell, Manos Kapritsos, Jacob R. Lorch, Bryan Parno, Michael L. Roberts, Srinath Setty, and Brian Zill. 2017. IronFleet: Proving Safety and Liveness of Practical Distributed Systems. Commun. ACM, 60, 7 (2017), June, 83–92. issn:0001-0782 https://doi.org/10.1145/3068608
[16]
Koen Jacobs, Dominique Devriese, and Amin Timany. 2022. Purity of an ST Monad: Full Abstraction by Semantically Typed Back-Translation. Proc. ACM Program. Lang., 6, OOPSLA1 (2022), Article 82, apr, 27 pages. https://doi.org/10.1145/3527326
[17]
Koen Jacobs, Amin Timany, and Dominique Devriese. 2021. Fully Abstract from Static to Gradual. Proc. ACM Program. Lang., 5, POPL (2021), Article 7, jan, 30 pages. https://doi.org/10.1145/3434288
[18]
Mauro Jaskelioff and Stephan Merz. 2005. Proving the Correctness of Disk Paxos. Arch. Formal Proofs, 2005 (2005), https://www.isa-afp.org/entries/DiskPaxos.shtml
[19]
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
[20]
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
[21]
Pertti Kellomäki. 2004. An Annotated Specification of the Consensus Protocol of Paxos Using Superposition in PVS. Tampere University of Technology. Institute of Software Systems.
[22]
Bernhard Kragl, Constantin Enea, Thomas A. Henzinger, Suha Orhun Mutluergil, and Shaz Qadeer. 2020. Inductive sequentialization of asynchronous programs. In Proceedings of the 41st ACM SIGPLAN International Conference on Programming Language Design and Implementation, PLDI 2020, London, UK, June 15-20, 2020. 227–242. https://doi.org/10.1145/3385412.3385980
[23]
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
[24]
Morten Krogh-Jespersen, Kasper Svendsen, and Lars Birkedal. 2017. A Relational Model of Types-and-Effects in Higher-Order Concurrent Separation Logic. In Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL ’17). Association for Computing Machinery, New York, NY, USA. 218–231. isbn:9781450346603 https://doi.org/10.1145/3009837.3009877
[25]
Morten Krogh-Jespersen, Amin Timany, Marit Edna Ohlenbusch, Simon Oddershede Gregersen, and Lars Birkedal. 2020. Aneris: A Mechanised Logic for Modular Reasoning about Distributed Systems. In Programming Languages and Systems - 29th European Symposium on Programming, ESOP 2020, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020, Dublin, Ireland, April 25-30, 2020, Proceedings. 336–365. https://doi.org/10.1007/978-3-030-44914-8_13
[26]
Leslie Lamport. 1992. Hybrid Systems in TLA^ +. In Hybrid Systems, Robert L. Grossman, Anil Nerode, Anders P. Ravn, and Hans Rischel (Eds.) (Lecture Notes in Computer Science, Vol. 736). Springer, 77–102. https://doi.org/10.1007/3-540-57318-6_25
[27]
Leslie Lamport. 1998. The Part-Time Parliament. ACM Trans. Comput. Syst., 16, 2 (1998), 133–169. https://doi.org/10.1145/279227.279229
[28]
Leslie Lamport. 2001. Paxos Made Simple. ACM SIGACT News (Distributed Computing Column) 32, 4 (Whole Number 121, December 2001), December, 51–58.
[29]
Hongjin Liang and Xinyu Feng. 2016. A program logic for concurrent objects under fair scheduling. 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, Rastislav Bodík and Rupak Majumdar (Eds.). ACM, 385–399. https://doi.org/10.1145/2837614.2837635
[30]
Hongjin Liang and Xinyu Feng. 2018. Progress of concurrent objects with partial methods. Proc. ACM Program. Lang., 2, POPL (2018), 20:1–20:31. https://doi.org/10.1145/3158108
[31]
Ognjen Maric, Christoph Sprenger, and David A. Basin. 2017. Cutoff Bounds for Consensus Algorithms. In Computer Aided Verification - 29th International Conference, CAV 2017, Heidelberg, Germany, July 24-28, 2017, Proceedings, Part II, Rupak Majumdar and Viktor Kuncak (Eds.) (Lecture Notes in Computer Science, Vol. 10427). Springer, 217–237. https://doi.org/10.1007/978-3-319-63390-9_12
[32]
Oded Padon, Giuliano Losa, Mooly Sagiv, and Sharon Shoham. 2017. Paxos made EPR: decidable reasoning about distributed protocols. Proc. ACM Program. Lang., 1, OOPSLA (2017), 108:1–108:31. https://doi.org/10.1145/3140568
[33]
Willem Penninckx, Bart Jacobs, and Frank Piessens. 2015. Sound, Modular and Compositional Verification of the Input/Output Behavior of Programs. In Programming Languages and Systems - 24th European Symposium on Programming, ESOP 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015. Proceedings, Jan Vitek (Ed.) (Lecture Notes in Computer Science, Vol. 9032). Springer, 158–182. https://doi.org/10.1007/978-3-662-46669-8_7
[34]
Marc Shapiro, Nuno M. Preguiça, Carlos Baquero, and Marek Zawirski. 2011. Convergent and Commutative Replicated Data Types. Bull. EATCS, 104 (2011), 67–88. http://eatcs.org/beatcs/index.php/beatcs/article/view/120
[35]
Simon Spies, Lennard Gäher, Daniel Gratzer, Joseph Tassarotti, Robbert Krebbers, Derek Dreyer, and Lars Birkedal. 2021. Transfinite Iris: resolving an existential dilemma of step-indexed separation logic. In PLDI ’21: 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Virtual Event, Canada, June 20-25, 20211. 80–95. https://doi.org/10.1145/3453483.3454031
[36]
Christoph Sprenger, Tobias Klenze, Marco Eilers, Felix A. Wolf, Peter Müller, Martin Clochard, and David Basin. 2020. Igloo: Soundly Linking Compositional Refinement and Separation Logic for Distributed System Verification. Proc. ACM Program. Lang., 4, OOPSLA (2020), Article 152, Nov., 31 pages. https://doi.org/10.1145/3428220
[37]
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
[38]
Joseph Tassarotti, Ralf Jung, and Robert Harper. 2017. A Higher-Order Logic for Concurrent Termination-Preserving Refinement. 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, Hongseok Yang (Ed.) (Lecture Notes in Computer Science, Vol. 10201). Springer, 909–936. https://doi.org/10.1007/978-3-662-54434-1_34
[39]
Amin Timany and Lars Birkedal. 2019. Mechanized Relational Verification of Concurrent Programs with Continuations. Proc. ACM Program. Lang., 3, ICFP (2019), Article 105, July, 28 pages. issn:2475-1421 https://doi.org/10.1145/3341709
[40]
Amin Timany, Simon Oddershede Gregersen, Léo Stefanesco, Jonas Kastberg Hinrichsen, Léon Gondelman, Abel Nieto, and Lars Birkedal. 2023. Trillium: Higher-Order Concurrent and Distributed Separation Logic for Intensional Refinement - Coq Artifact. https://doi.org/10.5281/zenodo.10100892
[41]
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. PACMPL, 2, POPL (2018), 64:1–64:28. https://doi.org/10.1145/3158152
[42]
Werner Vogels. 2009. Eventually consistent. Commun. ACM, 52, 1 (2009), 40–44. https://doi.org/10.1145/1435417.1435432
Index Terms
- Trillium: Higher-Order Concurrent and Distributed Separation Logic for Intensional Refinement
Recommendations
Interactive proofs in higher-order concurrent separation logic
POPL '17: Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming LanguagesWhen using a proof assistant to reason in an embedded logic -- like separation logic -- one cannot benefit from the proof contexts and basic tactics of the proof assistant. This results in proofs that are at a too low level of abstraction because they ...
Interactive proofs in higher-order concurrent separation logic
POPL '17When using a proof assistant to reason in an embedded logic -- like separation logic -- one cannot benefit from the proof contexts and basic tactics of the proof assistant. This results in proofs that are at a too low level of abstraction because they ...
Distributed causal memory: modular specification and verification in higher-order distributed separation logic
We present the first specification and verification of an implementation of a causally-consistent distributed database that supports modular verification of full functional correctness properties of clients and servers. We specify and reason about the ...
Comments
Information & Contributors
Information
Published In
January 2024
2820 pages
Copyright © 2024 Owner/Author.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 05 January 2024
Published in PACMPL Volume 8, Issue POPL
Check for updates
Badges
Author Tags
Qualifiers
- Research-article
Funding Sources
- VILLUM Foundation
- European Research Council
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 338Total Downloads
- Downloads (Last 12 months)338
- Downloads (Last 6 weeks)65
Reflects downloads up to 09 Nov 2024
Other Metrics
Citations
Cited By
View all- 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
View Options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in