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The next 700 relational program logics

Authors:

Kenji Maillard,

Cătălin Hriţcu,

Exequiel Rivas,

Antoine Van MuylderAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 4, Issue POPL

Article No.: 4, Pages 1 - 33

https://doi.org/10.1145/3371072

Published: 20 December 2019 Publication History

Abstract

We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an algebraic presentation of relational specifications as a class of relative monads, and link computations and specifications by introducing relational effect observations, which map pairs of monadic computations to relational specifications in a way that respects the algebraic structure. For an arbitrary relational effect observation, we generically define the core of a sound relational program logic, and explain how to complete it to a full-fledged logic for the monadic effect at hand. We show that this generic framework can be used to define relational program logics for effects as diverse as state, input-output, nondeterminism, and discrete probabilities. We, moreover, show that by instantiating our framework with state and unbounded iteration we can embed a variant of Benton's Relational Hoare Logic, and also sketch how to reconstruct Relational Hoare Type Theory. Finally, we identify and overcome conceptual challenges that prevented previous relational program logics from properly dealing with control effects, and are the first to provide a relational program logic for exceptions.

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References

[1]

C. Abate, R. Blanco, D. Garg, C. Hriţcu, M. Patrignani, and J. Thibault. Journey beyond full abstraction: Exploring robust property preservation for secure compilation . CSF, 2019. To Appear.

[2]

A. Aguirre, G. Barthe, M. Gaboardi, D. Garg, and P.-Y. Strub. A relational logic for higher-order programs . ICFP, 2017.

Digital Library

[3]

D. Ahman, C. Hriţcu, K. Maillard, G. Martínez, G. Plotkin, J. Protzenko, A. Rastogi, and N. Swamy. Dijkstra monads for free . POPL . 2017.

Digital Library

[4]

A. Ahmed, D. Dreyer, and A. Rossberg. State-dependent representation independence . POPL. 2009.

Digital Library

[5]

T. Altenkirch, J. Chapman, and T. Uustalu. Monads need not be endofunctors . LMCS, 11(1), 2015.

[6]

T. Antonopoulos, P. Gazzillo, M. Hicks, E. Koskinen, T. Terauchi, and S. Wei. Decomposition instead of self-composition for proving the absence of timing channels . PLDI . 2017.

Digital Library

[7]

P. Audebaud and C. Paulin-Mohring. Proofs of randomized algorithms in coq. In T. Uustalu, editor, Mathematics of Program Construction . 2006.

Digital Library

[8]

A. Banerjee, D. A. Naumann, and M. Nikouei. Relational logic with framing and hypotheses . FSTTCS. 2016.

[9]

G. Barthe, B. Grégoire, and S. Zanella-Béguelin. Formal certification of code-based cryptographic proofs . POPL, 2009.

Digital Library

[10]

G. Barthe, P. R. D’Argenio, and T. Rezk. Secure information flow by self-composition . MSCS, 21(6):1207–1252, 2011.

Digital Library

[11]

G. Barthe, F. Dupressoir, B. Grégoire, C. Kunz, B. Schmidt, and P. Strub. EasyCrypt: A tutorial . In A. Aldini, J. Lopez, and F. Martinelli, editors, Foundations of Security Analysis and Design VII - FOSAD 2012/2013 Tutorial Lectures. 2013a.

[12]

G. Barthe, B. Köpf, F. Olmedo, and S. Zanella-Béguelin. Probabilistic relational reasoning for differential privacy . TOPLAS, 35(3):9:1–9:49, 2013b.

Digital Library

[13]

G. Barthe, C. Fournet, B. Grégoire, P. Strub, N. Swamy, and S. Zanella-Béguelin. Probabilistic relational verification for cryptographic implementations . POPL. 2014.

Digital Library

[14]

G. Barthe, T. Espitau, B. Grégoire, J. Hsu, L. Stefanesco, and P. Strub. 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, 2015a.

Digital Library

[15]

G. Barthe, M. Gaboardi, E. J. G. Arias, J. Hsu, A. Roth, and P. Strub. Higher-order approximate relational refinement types for mechanism design and differential privacy . POPL. 2015b.

Digital Library

[16]

G. Barthe, J. M. Crespo, and C. Kunz. Product programs and relational program logics . JLAMP, 85(5):847–859, 2016.

[17]

G. Barthe, B. Grégoire, J. Hsu, and P. Strub. Coupling proofs are probabilistic product programs . POPL. 2017.

[18]

G. Barthe, R. Eilers, P. Georgiou, B. Gleiss, L. Kovács, and M. Maffei. Verifying relational properties using trace logic . Draft, 2019.

[19]

D. A. Basin, A. Lochbihler, and S. R. Sefidgar. CryptHOL: Game-based proofs in higher-order logic . IACR Cryptology ePrint Archive, 2017:753, 2017.

[20]

N. Benton. Simple relational correctness proofs for static analyses and program transformations . POPL. 2004.

Digital Library

[21]

N. Benton, J. Hughes, and E. Moggi. Monads and effects . APPSEM. 2000.

[22]

N. Benton, A. Kennedy, L. Beringer, and M. Hofmann. Relational semantics for effect-based program transformations: higher-order store . POPL. 2009.

Digital Library

[23]

N. Benton, M. Hofmann, and V. Nigam. Proof-relevant logical relations for name generation . TLCA. 2013.

[24]

N. Benton, M. Hofmann, and V. Nigam. Abstract effects and proof-relevant logical relations . POPL. 2014.

Digital Library

[25]

N. Benton, A. Kennedy, M. Hofmann, and V. Nigam. Counting successes: Effects and transformations for non-deterministic programs . In S. Lindley, C. McBride, P. W. Trinder, and D. Sannella, editors, A List of Successes That Can Change the World - Essays Dedicated to Philip Wadler on the Occasion of His 60th Birthday . 2016.

[26]

C. Berger, P.-A. Melliès, and M. Weber. Monads with arities and their associated theories . Journal of Pure and Applied Algebra, 216(8-9):2029–2048, 2012. New introduction; Section 1 shortened and redispatched with Section 2; Subsections on symmetric operads (3.14) and symmetric simplicial sets (4.17) added; Bibliography completed.

[27]

B. Blanchet, M. Abadi, and C. Fournet. Automated verification of selected equivalences for security protocols . J. Log. Algebr. Program., 75(1):3–51, 2008.

[28]

S. Boulier, P. Pédrot, and N. Tabareau. The next 700 syntactical models of type theory . CPP, 2017.

Digital Library

[29]

N. Bowler, S. Goncharov, P. B. Levy, and L. Schröder. Exploring the boundaries of monad tensorability on set . Logical Methods in Computer Science, 9(3), 2013.

[30]

M. Carbin, D. Kim, S. Misailovic, and M. C. Rinard. Proving acceptability properties of relaxed nondeterministic approximate programs . PLDI . 2012.

Digital Library

[31]

C. Casinghino, V. Sjöberg, and S. Weirich. Combining proofs and programs in a dependently typed language . In The 41st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL ’14, San Diego, CA, USA, January 20-21, 2014, 2014.

Digital Library

[32]

R. Chadha, V. Cheval, Ştefan Ciobâcă, and S. Kremer. Automated verification of equivalence properties of cryptographic protocols . ACM Trans. Comput. Log., 17(4):23:1–23:32, 2016.

Digital Library

[33]

E. Çiçek, G. Barthe, M. Gaboardi, D. Garg, and J. Hoffmann. Relational cost analysis . POPL, 2017.

[34]

M. R. Clarkson and F. B. Schneider. Hyperproperties . J. Comput. Secur., 18(6):1157–1210, 2010.

[35]

U. Dal Lago, F. Gavazzo, and P. B. Levy. Effectful applicative bisimilarity: Monads, relators, and Howe’s method . LICS. 2017.

[36]

G. A. Delbianco and A. Nanevski. Hoare-style reasoning with (algebraic) continuations . ICFP. 2013.

Digital Library

[37]

D. Dreyer, G. Neis, A. Rossberg, and L. Birkedal. A relational modal logic for higher-order stateful ADTs . POPL. 2010.

Digital Library

[38]

D. Dreyer, A. Ahmed, and L. Birkedal. Logical step-indexed logical relations . Logical Methods in Computer Science, 7(2), 2011.

[39]

D. Dreyer, G. Neis, and L. Birkedal. The impact of higher-order state and control effects on local relational reasoning . J. Funct. Program., 22(4-5):477–528, 2012.

Digital Library

[40]

M. Eilers, P. Müller, and S. Hitz. Modular product programs . In A. Ahmed, editor, 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 . 2018.

[41]

F. Faissole and B. Spitters. Synthetic topology in homotopy type theory for probabilistic programming . PPS 2017 - Workshop on probabilistic programming semantics, 2017. Poster.

[42]

A. Farzan and A. Vandikas. Automated hypersafety verification . In I. Dillig and S. Tasiran, editors, Computer Aided Verification - 31st International Conference, CAV 2019, New York City, NY, USA, July 15-18, 2019, Proceedings, Part I . 2019.

[43]

C. Führmann. Varieties of effects . FOSSACS, 2002.

[44]

M. Gaboardi, A. Haeberlen, J. Hsu, A. Narayan, and B. C. Pierce. Linear dependent types for differential privacy . POPL. 2013.

Digital Library

[45]

F. Gavazzo. Quantitative behavioural reasoning for higher-order effectful programs: Applicative distances . LICS. 2018.

Digital Library

[46]

T. Girka, D. Mentré, and Y. Régis-Gianas. A mechanically checked generation of correlating programs directed by structured syntactic differences . In Automated Technology for Verification and Analysis - 13th International Symposium, ATVA 2015, Shanghai, China, October 12-15, 2015, Proceedings, 2015.

[47]

T. Girka, D. Mentré, and Y. Régis-Gianas. Verifiable semantic difference languages . In Proceedings of the 19th International Symposium on Principles and Practice of Declarative Programming, Namur, Belgium, October 09 - 11, 2017, 2017.

Digital Library

[48]

M. Giry. A categorical approach to probability theory . Categorical Aspects of Topology and Analysis. 1982.

[49]

B. Godlin and O. Strichman. Inference rules for proving the equivalence of recursive procedures . In Z. Manna and D. A. Peled, editors, Time for Verification, Essays in Memory of Amir Pnueli. 2010.

[50]

N. Grimm, K. Maillard, C. Fournet, C. Hriţcu, M. Maffei, J. Protzenko, T. Ramananandro, A. Rastogi, N. Swamy, and S. ZanellaBéguelin. A monadic framework for relational verification: Applied to information security, program equivalence, and optimizations . CPP, 2018.

Digital Library

[51]

S. He, S. K. Lahiri, and Z. Rakamaric. Verifying relative safety, accuracy, and termination for program approximations . J. Autom. Reasoning, 60(1):23–42, 2018.

Digital Library

[52]

C. Hur, D. Dreyer, G. Neis, and V. Vafeiadis. The marriage of bisimulations and kripke logical relations . POPL. 2012.

Digital Library

[53]

C. Hur, G. Neis, D. Dreyer, and V. Vafeiadis. A logical step forward in parametric bisimulations . Technical Report MPI-SWS-2014-003, 2014.

[54]

B. Jacobs. Dijkstra and Hoare monads in monadic computation . Theor. Comput. Sci., 604:30–45, 2015.

Digital Library

[55]

C. Kapulkin and P. L. Lumsdaine. Homotopical inverse diagrams in categories with attributes, 2018.

[56]

S. Katsumata. Parametric effect monads and semantics of effect systems . POPL. 2014.

Digital Library

[57]

G. Kelly. Basic Concepts of Enriched Category Theory. Lecture note series / London mathematical society. Cambridge University Press, 1982.

[58]

V. Koutavas and M. Wand. Small bisimulations for reasoning about higher-order imperative programs . POPL. 2006.

Digital Library

[59]

S. Kundu, Z. Tatlock, and S. Lerner. Proving optimizations correct using parameterized program equivalence . PLDI . 2009.

Digital Library

[60]

S. K. Lahiri, C. Hawblitzel, M. Kawaguchi, and H. Rebêlo. SYMDIFF: A language-agnostic semantic diff tool for imperative programs . CAV . 2012.

Digital Library

[61]

A. Lochbihler. Effect polymorphism in higher-order logic (proof pearl) . JAR, 2018.

[62]

D. Lucanu and V. Rusu. Program equivalence by circular reasoning . Formal Asp. Comput., 27(4):701–726, 2015.

[63]

C. Lüth and N. Ghani. Composing monads using coproducts . ICFP. 2002.

Digital Library

[64]

K. Maillard, D. Ahman, R. Atkey, G. Martínez, C. Hriţcu, E. Rivas, and É. Tanter. Dijkstra monads for all . PACMPL, 3(ICFP): 104:1–104:29, 2019.

Digital Library

[65]

J. C. Mitchell. Representation independence and data abstraction . In POPL. 1986.

Digital Library

[66]

E. Moggi. Computational lambda-calculus and monads . LICS. 1989.

[67]

A. Nanevski, G. Morrisett, A. Shinnar, P. Govereau, and L. Birkedal. Ynot: dependent types for imperative programs . ICFP. 2008a.

Digital Library

[68]

A. Nanevski, J. G. Morrisett, and L. Birkedal. Hoare type theory, polymorphism and separation . JFP, 18(5-6):865–911, 2008b.

Digital Library

[69]

A. Nanevski, A. Banerjee, and D. Garg. Dependent type theory for verification of information flow and access control policies . ACM TOPLAS, 35(2):6, 2013.

Digital Library

[70]

D. A. Naumann. From coupling relations to mated invariants for checking information flow . ESORICS. 2006.

Digital Library

[71]

P. Pédrot and N. Tabareau. Failure is not an option - an exceptional type theory . ESOP, 2018.

[72]

A. Petcher and G. Morrisett. The foundational cryptography framework . POST . 2015.

Digital Library

[73]

G. D. Plotkin and J. Power. Notions of computation determine monads . FOSSACS, 2002.

[74]

G. D. Plotkin and M. Pretnar. Handlers of algebraic effects . ESOP. 2009.

Digital Library

[75]

W. Qu, M. Gaboardi, and D. Garg. Relational cost analysis for functional-imperative programs . To appear at ICFP, 2019.

[76]

I. Radicek, G. Barthe, M. Gaboardi, D. Garg, and F. Zuleger. Monadic refinements for relational cost analysis . PACMPL, 2 (POPL):36:1–36:32, 2018.

Digital Library

[77]

A. Sabelfeld and A. C. Myers. Language-based information-flow security . IEEE Journal on Selected Areas in Communications, 21(1):5–19, 2003.

Digital Library

[78]

D. Sangiorgi, N. Kobayashi, and E. Sumii. Environmental bisimulations for higher-order languages . ACM Trans. Program. Lang. Syst., 33(1):5:1–5:69, 2011.

Digital Library

[79]

T. Sato, A. Aguirre, G. Barthe, M. Gaboardi, D. Garg, and J. Hsu. Formal verification of higher-order probabilistic programs: reasoning about approximation, convergence, bayesian inference, and optimization . PACMPL, 3(POPL):38:1–38:30, 2019.

Digital Library

[80]

M. Shulman. Univalence for inverse diagrams and homotopy canonicity . Mathematical Structures in Computer Science, 25: 1203–1277, 2014.

[81]

M. Sousa and I. Dillig. Cartesian Hoare logic for verifying k-safety properties . PLDI . 2016.

Digital Library

[82]

R. Street. The formal theory of monads . Journal of Pure and Applied Algebra, 2, 1972.

[83]

E. Sumii. A complete characterization of observational equivalence in polymorphic lambda-calculus with general references . CSL . 2009.

[84]

N. Swamy, J. Weinberger, C. Schlesinger, J. Chen, and B. Livshits. Verifying higher-order programs with the Dijkstra monad . PLDI, 2013.

Digital Library

[85]

N. Swamy, C. Hriţcu, C. Keller, A. Rastogi, A. Delignat-Lavaud, S. Forest, K. Bhargavan, C. Fournet, P.-Y. Strub, M. Kohlweiss, J.-K. Zinzindohoué, and S. Zanella-Béguelin. Dependent types and multi-monadic effects in F* . POPL. 2016.

[86]

T. Terauchi and A. Aiken. Secure information flow as a safety problem . SAS. 2005.

Digital Library

[87]

A. Timany and L. Birkedal. Mechanized relational verification of concurrent programs with continuations . To appear at ICFP, 2019.

[88]

A. Timany, L. Stefanesco, M. Krogh-Jespersen, and L. Birkedal. A logical relation for monadic encapsulation of state: proving contextual equivalences in the presence of runST . PACMPL, 2(POPL):64:1–64:28, 2018.

Digital Library

[89]

S. Tonelli. Investigations into a model of type theory based on the concept of basic pair . Master’s thesis, Stockholm University, 2013. supervisors Erik Palmgren and Giovanni Sambin.

[90]

D. Unruh. Quantum relational Hoare logic . PACMPL, 3(POPL):33:1–33:31, 2019.

Digital Library

[91]

Y. Wang, I. Dillig, S. K. Lahiri, and W. R. Cook. Verifying equivalence of database-driven applications . PACMPL, 2(POPL): 56:1–56:29, 2018.

Digital Library

[92]

D. Winograd-Cort, A. Haeberlen, A. Roth, and B. C. Pierce. A framework for adaptive differential privacy . PACMPL, 1(ICFP): 10:1–10:29, 2017.

Digital Library

[93]

H. Yang. Relational separation logic . Theor. Comput. Sci., 375(1-3):308–334, 2007.

Digital Library

[94]

H. Yasuoka and T. Terauchi. Quantitative information flow as safety and liveness hyperproperties . Theor. Comput. Sci., 538: 167–182, 2014.

[95]

A. Zaks and A. Pnueli. CoVaC: Compiler validation by program analysis of the cross-product . FM. 2008.

Digital Library

[96]

N. Zeilberger. The Logical Basis of Evaluation Order and Pattern-Matching . PhD thesis, Carnegie Mellon University, 2009.

[97]

D. Zhang and D. Kifer. LightDP: towards automating differential privacy proofs . POPL. 2017.

[98]

H. Zhang, E. Roth, A. Haeberlen, B. C. Pierce, and A. Roth. Fuzzi: A three-level logic for differential privacy . CoRR, abs/1905.12594, 2019.

Cited By

Haselwarter PLi KAguirre AGregersen STassarotti JBirkedal L(2025)Approximate Relational Reasoning for Higher-Order Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/37048779:POPL(1196-1226)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704877
Dardinier TLi AMüller P(2024)Hypra: A Deductive Program Verifier for Hyper Hoare LogicProceedings of the ACM on Programming Languages10.1145/36897568:OOPSLA2(1279-1308)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689756
Zhang LZilberstein NKaminski BSilva A(2024)Quantitative Weakest Hyper Pre: Unifying Correctness and Incorrectness Hyperproperties via Predicate TransformersProceedings of the ACM on Programming Languages10.1145/36897408:OOPSLA2(817-845)Online publication date: 8-Oct-2024
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Index Terms

The next 700 relational program logics
1. Theory of computation
  1. Logic
    1. Hoare logic
    2. Type theory
  2. Semantics and reasoning
    1. Program reasoning
    2. Program semantics
      1. Categorical semantics

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 4, Issue POPL

January 2020

1984 pages

EISSN:2475-1421

DOI:10.1145/3377388

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Published: 20 December 2019

Published in PACMPL Volume 4, Issue POPL

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Haselwarter PLi KAguirre AGregersen STassarotti JBirkedal L(2025)Approximate Relational Reasoning for Higher-Order Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/37048779:POPL(1196-1226)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704877
Dardinier TLi AMüller P(2024)Hypra: A Deductive Program Verifier for Hyper Hoare LogicProceedings of the ACM on Programming Languages10.1145/36897568:OOPSLA2(1279-1308)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689756
Zhang LZilberstein NKaminski BSilva A(2024)Quantitative Weakest Hyper Pre: Unifying Correctness and Incorrectness Hyperproperties via Predicate TransformersProceedings of the ACM on Programming Languages10.1145/36897408:OOPSLA2(817-845)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689740
Dardinier TMüller P(2024)Hyper Hoare Logic: (Dis-)Proving Program HyperpropertiesProceedings of the ACM on Programming Languages10.1145/36564378:PLDI(1485-1509)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656437
Andrici CCiobâcă ȘHriţcu CMartínez GRivas ETanter ÉWinterhalter T(2024)Securing Verified IO Programs Against Unverified Code in F*Proceedings of the ACM on Programming Languages10.1145/36329168:POPL(2226-2259)Online publication date: 5-Jan-2024
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Haselwarter PRivas EVan Muylder AWinterhalter TAbate CSidorenco NHriţcu CMaillard KSpitters B(2023)SSProve: A Foundational Framework for Modular Cryptographic Proofs in CoqACM Transactions on Programming Languages and Systems10.1145/359473545:3(1-61)Online publication date: 20-Jul-2023
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Chappe NHe PHenrio LZakowski YZdancewic S(2023)Choice Trees: Representing Nondeterministic, Recursive, and Impure Programs in CoqProceedings of the ACM on Programming Languages10.1145/35712547:POPL(1770-1800)Online publication date: 11-Jan-2023
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Antonopoulos TKoskinen ELe TNagasamudram RNaumann DNgo M(2023)An Algebra of Alignment for Relational VerificationProceedings of the ACM on Programming Languages10.1145/35712137:POPL(573-603)Online publication date: 11-Jan-2023
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Banerjee ANagasamudram RNaumann DNikouei M(2023)A Relational Program Logic with Data Abstraction and Dynamic FramingACM Transactions on Programming Languages and Systems10.1145/355149744:4(1-136)Online publication date: 10-Jan-2023
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