research-article

Characteristic formulae for the verification of imperative programs

Author:

Arthur CharguéraudAuthors Info & Claims

ICFP '11: Proceedings of the 16th ACM SIGPLAN international conference on Functional programming

Pages 418 - 430

https://doi.org/10.1145/2034773.2034828

Published: 19 September 2011 Publication History

Abstract

In previous work, we introduced an approach to program verification based on characteristic formulae. The approach consists of generating a higher-order logic formula from the source code of a program. This characteristic formula is constructed in such a way that it gives a sound and complete description of the semantics of that program. The formula can thus be exploited in an interactive proof assistant to formally verify that the program satisfies a particular specification.

This previous work was, however, only concerned with purely-functional programs. In the present paper, we describe the generalization of characteristic formulae to an imperative programming language. In this setting, characteristic formulae involve specifications expressed in the style of Separation Logic. They also integrate the frame rule, which enables local reasoning. We have implemented a tool based on characteristic formulae. This tool, called CFML, supports the verification of imperative Caml programs using the Coq proof assistant. Using CFML, we have formally verified nontrivial imperative algorithms, as well as CPS functions, higher-order iterators, and programs involving higher-order stores.

Supplementary Material

MP4 File (_talk13.mp4)

Download
53.54 MB

References

[1]

Andrew W. Appel. Tactics for separation logic. Unpublished draft, http://www.cs.princeton.edu/appel/papers/septacs.pdf, 2006.

[2]

Mike Barnett, Rob DeLine, Manuel Fähndrich, K. Rustan M. Leino, and Wolfram Schulte. Verification of object-oriented programs with invariants. Journal of Object Technology, 3(6), 2004.

[3]

Bruno Barras and Bruno Bernardo. The implicit calculus of constructions as a programming language with dependent types. In FoSSaCS, volume 4962 of LNCS, pages 365--379. Springer, 2008.

Digital Library

[4]

Bernhard Beckert, Reiner Hähnle, and Peter H. Schmitt. Verification of Object-Oriented Software: The KeY Approach, volume 4334 of LNCS. Springer-Verlag, Berlin, 2007.

Digital Library

[5]

Josh Berdine, Cristiano Calcagno, and Peter W. O'Hearn. Smallfoot: Modular automatic assertion checking with separation logic. In International Symposium on Formal Methods for Components and Objects, volume 4111 of LNCS, pages 115--137. Springer, 2005.

Digital Library

[6]

Martin Berger, Kohei Honda, and Nobuko Yoshida. A logical analysis of aliasing in imperative higher-order functions. In ICFP, pages 280--293, 2005.

Digital Library

[7]

Arthur Charguéraud. Verification of call-by-value functional programs through a deep embedding. 2009. Unpublished. http://arthur.chargueraud.org/research/2009/deep/.

[8]

Arthur Charguéraud. Characteristic Formulae for Mechanized Program Verification. PhD thesis, Université Paris-Diderot, 2010.

[9]

Arthur Charguéraud. Program verification through characteristic formulae. In ICFP, pages 321--332. ACM, 2010.

Digital Library

[10]

Adam Chlipala, Gregory Malecha, Greg Morrisett, Avraham Shinnar, and Ryan Wisnesky. Effective interactive proofs for higher-order imperative programs. In ICFP, 2009.

Digital Library

[11]

The Coq Development Team. The Coq Proof Assistant Reference Manual, Version 8.2, 2009.

[12]

Jean-Christophe Filliâtre. Verification of non-functional programs using interpretations in type theory. Journal of Functional Programming, 13(4):709--745, 2003.

Digital Library

[13]

Cormac Flanagan, Amr Sabry, Bruce F. Duba, and Matthias Felleisen. The essence of compiling with continuations. In PLDI, pages 237--247, 1993.

Digital Library

[14]

Susanne Graf and Joseph Sifakis. A modal characterization of observational congruence on finite terms of CCS. Information and Control, 68(1-3):125--145, 1986.

Digital Library

[15]

David Harel, Dexter Kozen, and Jerzy Tiuryn. Dynamic Logic. The MIT Press, Cambridge, Massachusetts, 2000.

[16]

Matthew Hennessy and Robin Milner. On observing nondeterminism and concurrency. In ICALP, volume 85 of LNCS, pages 299--309. Springer-Verlag, 1980.

Digital Library

[17]

C. A. R. Hoare. An axiomatic basis for computer programming. Communications of the ACM, 12(10):576--580, 583, 1969.

Digital Library

[18]

Kohei Honda, Martin Berger, and Nobuko Yoshida. Descriptive and relative completeness of logics for higher-order functions. In ICALP, volume 4052 of LNCS. Springer, 2006.

Digital Library

[19]

Bart Jacobs and Erik Poll. Java program verification at nijmegen: Developments and perspective. In ISSS, volume 3233 of LNCS, pages 134--153. Springer, 2003.

[20]

Johannes Kanig and Jean-Christophe Filliâtre. Who: a verifier for effectful higher-order programs. In ML'09: Proceedings of the 2009 ACM SIGPLAN workshop on ML, pages 39--48. ACM, 2009.

Digital Library

[21]

Gerwin Klein, Philip Derrin, and Kevin Elphinstone. Experience report: seL4: formally verifying a high-performance microkernel. In ICFP, pages 91--96. ACM, 2009.

Digital Library

[22]

Gerwin Klein, Kevin Elphinstone, Gernot Heiser, June Andronick, David Cock, Philip Derrin, Dhammika Elkaduwe, Kai Engelhardt, Rafal Kolanski, Michael Norrish, Thomas Sewell, Harvey Tuch, and Simon Winwood. seL4: Formal verification of an OS kernel. In Proceedings of the 22nd Symposium on Operating Systems Principles (SOSP), Operating Systems Review (OSR), pages 207--220, Big Sky, MT, 2009. ACM SIGOPS.

Digital Library

[23]

Xavier Leroy. Formal certification of a compiler back-end or: programming a compiler with a proof assistant. In POPL, pages 42--54, 2006.

Digital Library

[24]

Xavier Leroy, Damien Doligez, Jacques Garrigue, Didier Rémy, and Jérôme Vouillon. The Objective Caml system, 2005.

[25]

Pierre Letouzey. Programmation fonctionnelle certifiée - l'extraction de programmes dans l'assistant Coq. PhD thesis, Université Paris 11, 2004.

[26]

Nicolas Marti, Reynald Affeldt, and Akinori Yonezawa. Towards formal verification of memory properties using separation logic, 2005.

[27]

Andrew McCreight. Practical tactics for separation logic. In TPHOLs, volume 5674 of LNCS, pages 343--358. Springer, 2009.

Digital Library

[28]

Farhad Mehta and Tobias Nipkow. Proving pointer programs in higher-order logic. Information and Computation, 199(1-2), 2005.

Digital Library

[29]

Magnus O. Myreen. Formal Verification of Machine-Code Programs. PhD thesis, University of Cambridge, 2008.

[30]

Magnus O. Myreen. Separation logic adapted for proofs by rewriting. In Interactive Theorem Proving (ITP), volume 6172 of LNCS, pages 485--489. Springer, 2010.

Digital Library

[31]

Magnus O. Myreen and Michael J. C. Gordon. Verified LISP implementations on ARM, x86 and powerPC. In TPHOLs, volume 5674 of LNCS, pages 359--374. Springer, 2009.

Digital Library

[32]

Aleksandar Nanevski and Greg Morrisett. Dependent type theory of stateful higher-order functions. Technical Report TR-24-05, Harvard University, 2005.

[33]

Aleksandar Nanevski, J. Gregory Morrisett, and Lars Birkedal. Hoare type theory, polymorphism and separation. Journal of Functional Programming, 18(5--6):865--911, 2008.

Digital Library

[34]

Aleksandar Nanevski, Viktor Vafeiadis, and Josh Berdine. Structuring the verification of heap-manipulating programs. In POPL, pages 261--274. ACM, 2010.

Digital Library

[35]

Zhaozhong Ni and Zhong Shao. Certified assembly programming with embedded code pointers. In POPL, 2006.

Digital Library

[36]

Peter O'Hearn, John Reynolds, and Hongseok Yang. Local reasoning about programs that alter data structures. In CSL, volume 2142 of LNCS, pages 1--19, Berlin, 2001. Springer-Verlag.

Digital Library

[37]

Chris Okasaki. Purely Functional Data Structures. Cambridge University Press, 1999.

Digital Library

[38]

Yann Régis-Gianas and François Pottier. A Hoare logic for call-by-value functional programs. In MPC, 2008.

Digital Library

[39]

John C. Reynolds. Separation logic: A logic for shared mutable data structures. In LICS, pages 55--74, 2002.

Digital Library

[40]

Hayo Thielecke. Frame rules from answer types for code pointers. In POPL, pages 309--319, 2006.

Digital Library

[41]

Thomas Tuerk. Local reasoning about while-loops. In VSTTE LNCS, 2010.

[42]

Karen Zee, Viktor Kuncak, and Martin C. Rinard. An integrated proof language for imperative programs. In PLDI, pages 338--351. ACM, 2009.

Digital Library

Cited By

Spies SGäher LSammler MDreyer D(2024)Quiver: Guided Abductive Inference of Separation Logic Specifications in CoqProceedings of the ACM on Programming Languages10.1145/36564138:PLDI(889-913)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656413
Gladshtein VZhao QAhrens WAmarasinghe SSergey I(2024)Mechanised Hypersafety Proofs about Structured DataProceedings of the ACM on Programming Languages10.1145/36564038:PLDI(647-670)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656403
Wang ZCao QTao Y(2024)Verifying Programs with Logic and Extended Proof Rules: Deep Embedding vs. Shallow EmbeddingJournal of Automated Reasoning10.1007/s10817-024-09706-568:3Online publication date: 10-Aug-2024
https://doi.org/10.1007/s10817-024-09706-5
Show More Cited By

Index Terms

Characteristic formulae for the verification of imperative programs
1. Software and its engineering
  1. Software creation and management
    1. Software verification and validation
      1. Formal software verification
  2. Software organization and properties
    1. Software functional properties
      1. Formal methods

Recommendations

Program verification through characteristic formulae
ICFP '10: Proceedings of the 15th ACM SIGPLAN international conference on Functional programming

This paper describes CFML, the first program verification tool based on characteristic formulae. Given the source code of a pure Caml program, this tool generates a logical formula that implies any valid post-condition for that program. One can then ...
Characteristic formulae for the verification of imperative programs
ICFP '11

In previous work, we introduced an approach to program verification based on characteristic formulae. The approach consists of generating a higher-order logic formula from the source code of a program. This characteristic formula is constructed in such ...
Program verification through characteristic formulae
ICFP '10

This paper describes CFML, the first program verification tool based on characteristic formulae. Given the source code of a pure Caml program, this tool generates a logical formula that implies any valid post-condition for that program. One can then ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

ICFP '11: Proceedings of the 16th ACM SIGPLAN international conference on Functional programming

September 2011

470 pages

ISBN:9781450308656

DOI:10.1145/2034773

General Chairs:
Manuel Chakravarty
University of New South Wales, Australia
,
Zhenjiang Hu
National Institute of Informatics, Japan
,
Program Chair:
Olivier Danvy
Aarhus University, Denmark

ACM SIGPLAN Notices Volume 46, Issue 9
ICFP '11
September 2011
456 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2034574
Issue’s Table of Contents

Copyright © 2011 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGPLAN: ACM Special Interest Group on Programming Languages

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 19 September 2011

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

ICFP '11

Sponsor:

SIGPLAN

ICFP '11: ACM SIGPLAN International Conference on Functional Programming

September 19 - 21, 2011

Tokyo, Japan

Acceptance Rates

ICFP '11 Paper Acceptance Rate 33 of 92 submissions, 36%;

Overall Acceptance Rate 333 of 1,064 submissions, 31%

Upcoming Conference

ICFP '25

Sponsor:
sigplan

ACM SIGPLAN International Conference on Functional Programming

October 12 - 18, 2025

Singapore , Singapore

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

62
Total Citations
View Citations
322
Total Downloads

Downloads (Last 12 months)18
Downloads (Last 6 weeks)0

Reflects downloads up to 25 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Spies SGäher LSammler MDreyer D(2024)Quiver: Guided Abductive Inference of Separation Logic Specifications in CoqProceedings of the ACM on Programming Languages10.1145/36564138:PLDI(889-913)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656413
Gladshtein VZhao QAhrens WAmarasinghe SSergey I(2024)Mechanised Hypersafety Proofs about Structured DataProceedings of the ACM on Programming Languages10.1145/36564038:PLDI(647-670)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656403
Wang ZCao QTao Y(2024)Verifying Programs with Logic and Extended Proof Rules: Deep Embedding vs. Shallow EmbeddingJournal of Automated Reasoning10.1007/s10817-024-09706-568:3Online publication date: 10-Aug-2024
https://doi.org/10.1007/s10817-024-09706-5
Pereira M(2024)Practical Deductive Verification of OCaml ProgramsFormal Methods10.1007/978-3-031-71177-0_29(518-542)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-71177-0_29
Gopinathan KKeoliya MSergey I(2023)Mostly Automated Proof Repair for Verified LibrariesProceedings of the ACM on Programming Languages10.1145/35912217:PLDI(25-49)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1145/3591221
Charguéraud AChlipala AErbsen AGruetter S(2023)Omnisemantics: Smooth Handling of NondeterminismACM Transactions on Programming Languages and Systems10.1145/357983445:1(1-43)Online publication date: 8-Mar-2023
https://dl.acm.org/doi/10.1145/3579834
Giet JRidoux FRival X(2023)A Product of Shape and Sequence AbstractionsStatic Analysis10.1007/978-3-031-44245-2_15(310-342)Online publication date: 24-Oct-2023
https://doi.org/10.1007/978-3-031-44245-2_15
Denis XJourdan J(2023)Specifying and Verifying Higher-order Rust IteratorsTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-031-30820-8_9(93-110)Online publication date: 22-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-30820-8_9
Appel APopescu AZdancewic S(2022)Coq’s vibrant ecosystem for verification engineering (invited talk)Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3497775.3503951(2-11)Online publication date: 17-Jan-2022
https://dl.acm.org/doi/10.1145/3497775.3503951
Fromherz ARastogi ASwamy NGibson SMartínez GMerigoux DRamananandro T(2021)Steel: proof-oriented programming in a dependently typed concurrent separation logicProceedings of the ACM on Programming Languages10.1145/34735905:ICFP(1-30)Online publication date: 19-Aug-2021
https://dl.acm.org/doi/10.1145/3473590
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten