research-article

Compositional higher-order model checking via ω-regular games over Böhm trees

Authors:

Takeshi Tsukada,

C.-H. Luke OngAuthors Info & Claims

CSL-LICS '14: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

Article No.: 78, Pages 1 - 10

https://doi.org/10.1145/2603088.2603133

Published: 14 July 2014 Publication History

Abstract

We introduce type-checking games, which are ω-regular games over Böhm trees, determined by a type of the Kobayashi-Ong intersection type system. These games are a higher-type extension of parity games over trees, determined by an alternating parity tree automaton. However, in contrast to these games over trees, the "game boards" of our type-checking games are composable, using the composition of Böhm trees. Moreover the winner (and winning strategies) of a composite game is completely determined by the respective winners (and winning strategies) of the component games.

To our knowledge, type-checking games give the first compositional analysis of higher-order model checking, or the model checking of trees generated by recursion schemes. We study a higher-type analogue of higher-order model checking, namely, the problem to decide the winner of a type-checking game over the Böhm tree generated by an arbitrary λY-term. We introduce a new type-assignment system and use it to prove that the problem is decidable.

On the semantic side, we develop a novel (two-level) arena game model for type-checking games, which is a cartesian closed category equipped with parametric monad and comonad that themselves form a parametrised adjunction.

References

[1]

C. H. Broadbent, A. Carayol, C.-H. L. Ong, and O. Serre. Recursion schemes and logical reflection. In Proceedings of the 25th Annual IEEE Symposium on Logic in Computer Science (LICS 2010), pages 120--129. IEEE Computer Society, 2010.

Digital Library

[2]

A. Carayol and O. Serre. Collapsible pushdown automata and labeled recursion schemes: Equivalence, safety and effective selection. In Proceedings of the 27th Annual IEEE Symposium on Logic in Computer Science (LICS 2012), pages 165--174. IEEE Computer Society, 2012.

Digital Library

[3]

P. Clairambault and R. Harmer. Totality in arena games. Ann. Pure Appl. Logic, 161(5):673--689, 2010.

[4]

P. Clairambault and A. S. Murawski. Böhm trees as higher-order recursive schemes. In Proceedings of IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013), volume 24 of LIPIcs, pages 91--102. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2013.

[5]

P.-L. Curien. Abstract Böhm trees. Mathematical Structures in Computer Science, 8(6):559--591, 1998.

Digital Library

[6]

K. Fujima, S. Ito, and N. Kobayashi. Practical alternating parity tree automata model checking of higher-order recursion schemes. In Proceedings of 11th Asian Symposium on Programming Languages and Systems (APLAS 2013), volume 8301 of LNCS. Springer, 2013. ISBN 978-3-319-03541-3.

Digital Library

[7]

A. Haddad. Model checking and functional program transformations. In Proceedings of IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013), volume 24 of LIPIcs, pages 115--126. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2013.

[8]

M. Hague, A. S. Murawski, C.-H. L. Ong, and O. Serre. Collapsible pushdown automata and recursion schemes. In Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 2008), pages 452--461. IEEE Computer Society, 2008.

Digital Library

[9]

J. M. E. Hyland and C.-H. L. Ong. On full abstraction for PCF: I, II, and III. Inf. Comput., 163(2):285--408, 2000.

Digital Library

[10]

N. Kobayashi. Model checking higher-order programs. J. ACM, 60 (3):20, 2013.

Digital Library

[11]

N. Kobayashi and C.-H. L. Ong. A type system equivalent to the modal mu-calculus model checking of higher-order recursion schemes. In Proceedings of the 24th Annual IEEE Symposium on Logic in Computer Science (LICS 2009), pages 179--188. IEEE Computer Society, 2009.

Digital Library

[12]

N. Kobayashi, K. Matsuda, and A. Shinohara. Functional programs as compressed data. In Proceedings of the ACM SIGPLAN 2012 Workshop on Partial Evaluation and Program Manipulation (PEPM 2012), pages 121--130. ACM, 2012.

Digital Library

[13]

P.-A. Melliès. Asynchronous games 2: The true concurrency of innocence. Theor. Comput. Sci., 358(2-3):200--228, 2006.

Digital Library

[14]

P.-A. Melliès. Parametric monads and enriched adjunctions. Preprint, 28 pages, 2012.

[15]

C.-H. L. Ong. On model-checking trees generated by higher-order recursion schemes. In Proceedings of 21th IEEE Symposium on Logic in Computer Science (LICS 2006), pages 81--90. IEEE Computer Society, 2006.

Digital Library

[16]

C.-H. L. Ong and T. Tsukada. Two-level game semantics, intersection types, and recursion schemes. In Proceedings of 39th International Colloquium on Automata, Languages, and Programming (ICALP 2012), volume 7392 of LNCS, pages 325--336. Springer, 2012.

Digital Library

[17]

D. Perrin and J. Pin. Infinite Words: Automata, Semigroups, Logic and Games. Academic Press, 2004.

[18]

S. J. Ramsay, R. P. Neatherway, and C.-H. L. Ong. A type-directed abstraction refinement approach to higher-order model checking. In Proceedings of the 41st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 2014), pages 61--72. ACM, 2014.

Digital Library

[19]

S. Salvati and I. Walukiewicz. Krivine machines and higher-order schemes. In Proceedings of the 38th International Colloquium on Automata, Languages and Programming (ICALP 2011), volume 6756 of LNCS, pages 162--173. Springer, 2011.

Digital Library

[20]

S. Salvati and I. Walukiewicz. Evaluation is MSOL-compatible. In Proceedings of IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013), volume 24 of LIPIcs, pages 103--114. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2013.

[21]

C. Stirling. Dependency tree automata. In Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures (FoSSaCS 2009), volume 5504 of LNCS, pages 92--106. Springer, 2009.

Digital Library

[22]

T. Tsukada and C.-H. L. Ong. Compositional higher-order model-checking via ω-regular games over Böhm trees (long version). Preprint, 2014. URL http://www.kb.is.s.u-tokyo.ac.jp/~tsukada/papers/effect-arena-long.pdf.

[23]

S. van Bakel. The heart of intersection type assignment: Normalisation proofs revisited. Theor. Comput. Sci., 398(1-3):82--94, 2008.

Digital Library

Cited By

Sekiyama TUnno H(2025)Algebraic Temporal Effects: Temporal Verification of Recursively Typed Higher-Order ProgramsProceedings of the ACM on Programming Languages10.1145/37049149:POPL(2306-2336)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704914
Watanabe KEberhart CAsada KHasuo I(2024)Compositional Solution of Mean Payoff Games by String DiagramsPrinciples of Verification: Cycling the Probabilistic Landscape10.1007/978-3-031-75778-5_20(423-445)Online publication date: 18-Nov-2024
https://doi.org/10.1007/978-3-031-75778-5_20
Watanabe KEberhart CAsada KHasuo I(2023)Compositional Probabilistic Model Checking with String Diagrams of MDPsComputer Aided Verification10.1007/978-3-031-37709-9_3(40-61)Online publication date: 17-Jul-2023
https://doi.org/10.1007/978-3-031-37709-9_3
Show More Cited By

Index Terms

Compositional higher-order model checking via ω-regular games over Böhm trees
1. Software and its engineering
  1. Software organization and properties
    1. Software functional properties
      1. Formal methods
        Model checking
2. Theory of computation
  1. Logic
    1. Verification by model checking
  2. Semantics and reasoning
    1. Program reasoning

Recommendations

Böhm theorem and Böhm trees for the Λμ-calculus

Parigot's @l@m-calculus (Parigot, 1992 [1]) is now a standard reference about the computational content of classical logic as well as for the formal study of control operators in functional languages. In addition to the fine-grained Curry-Howard ...
Abstract Böhm trees

We present a formalism of trees with pointers, called abstract Böhm trees, that provide a suitable abstract framework in which various cut-free proofs or normal terms of several λ-calculus based languages (including PCF and Parigot's λμ-calculus) can be ...
Predicate abstraction and CEGAR for higher-order model checking
PLDI '11: Proceedings of the 32nd ACM SIGPLAN Conference on Programming Language Design and Implementation

Higher-order model checking (more precisely, the model checking of higher-order recursion schemes) has been extensively studied recently, which can automatically decide properties of programs written in the simply-typed λ-calculus with recursion and ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

CSL-LICS '14: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

July 2014

764 pages

ISBN:9781450328869

DOI:10.1145/2603088

Program Chairs:
Thomas Henzinger
Institute of Science and Technology (IST), Austria
,
Dale Miller
INRIA and LIX/Ecole Polytechnique, Palaiseau

Copyright © 2014 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

SIGLOG: ACM Special Interest Group on Logic and Computation
EACSL: European Association for Computer Science Logic
IEEE-CS\DATC: IEEE Computer Society

In-Cooperation

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 14 July 2014

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

Japan Society for the Promotion of Science

Conference

CSL-LICS '14

Sponsor:

SIGLOG
EACSL
IEEE-CS\DATC

CSL-LICS '14: JOINT MEETING OF the Twenty-Third EACSL Annual Conference on COMPUTER SCIENCE LOGIC

July 14 - 18, 2014

Vienna, Austria

Acceptance Rates

CSL-LICS '14 Paper Acceptance Rate 74 of 212 submissions, 35%;

Overall Acceptance Rate 215 of 622 submissions, 35%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

20
Total Citations
View Citations
161
Total Downloads

Downloads (Last 12 months)6
Downloads (Last 6 weeks)1

Reflects downloads up to 08 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Sekiyama TUnno H(2025)Algebraic Temporal Effects: Temporal Verification of Recursively Typed Higher-Order ProgramsProceedings of the ACM on Programming Languages10.1145/37049149:POPL(2306-2336)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704914
Watanabe KEberhart CAsada KHasuo I(2024)Compositional Solution of Mean Payoff Games by String DiagramsPrinciples of Verification: Cycling the Probabilistic Landscape10.1007/978-3-031-75778-5_20(423-445)Online publication date: 18-Nov-2024
https://doi.org/10.1007/978-3-031-75778-5_20
Watanabe KEberhart CAsada KHasuo I(2023)Compositional Probabilistic Model Checking with String Diagrams of MDPsComputer Aided Verification10.1007/978-3-031-37709-9_3(40-61)Online publication date: 17-Jul-2023
https://doi.org/10.1007/978-3-031-37709-9_3
Watanabe KEberhart CAsada KHasuo I(2021)A Compositional Approach to Parity GamesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.351.17351(278-295)Online publication date: 29-Dec-2021
https://doi.org/10.4204/EPTCS.351.17
Yang FFerlini AAguiari DPesavento DTse RBanerjee SXie GPau G(2021)Revisiting WiFi offloading in the wild for V2I applicationsComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2021.108634202:COnline publication date: 30-Dec-2021
https://dl.acm.org/doi/10.1016/j.comnet.2021.108634
Kobayashi NLago UGrellois CBouyer P(2019)On the termination problem for probabilistic higher-order recursive programsProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470177(1-14)Online publication date: 24-Jun-2019
https://dl.acm.org/doi/10.5555/3470152.3470177
Kobayashi NTsukada TWatanabe K(2018)Higher-Order Program Verification via HFL Model CheckingProgramming Languages and Systems10.1007/978-3-319-89884-1_25(711-738)Online publication date: 14-Apr-2018
https://doi.org/10.1007/978-3-319-89884-1_25
Kobayashi NLozes ÉBruse F(2017)On the relationship between higher-order recursion schemes and higher-order fixpoint logicACM SIGPLAN Notices10.1145/3093333.300985452:1(246-259)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009854
Kobayashi NLozes ÉBruse FCastagna GGordon A(2017)On the relationship between higher-order recursion schemes and higher-order fixpoint logicProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009854(246-259)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3009837.3009854
Li YHuang SFan RZhang ZZhou Y(2017)Research on gateway deployment of WMN based on maximum coupling subgraph and PSO algorithmSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-015-1822-221:4(923-933)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1007/s00500-015-1822-2
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