Temporal verification of higher-order functional programs

Akihiro Murase, Tachio Terauchi, Naoki Kobayashi, Ryosuke Sato, Hiroshi Unno

研究成果: Article

4 引用 (Scopus)

抄録

We present an automated approach to verifying arbitrary omega regular properties of higher-order functional programs. Previous automated methods proposed for this class of programs could only handle safety properties or termination, and our approach is the first to be able to verify arbitrary omega-regular liveness properties. Our approach is automata-theoretic, and extends our recent work on binary-reachability-based approach to automated termination verification of higher-order functional programs to fair termination published in ESOP 2014. In that work, we have shown that checking disjunctive well-foundedness of (the transitive closure of) the "calling relation" is sound and complete for termination. The extension to fair termination is tricky, however, because the straightforward extension that checks disjunctive well-foundedness of the fair calling relation turns out to be unsound, as we shall show in the paper. Roughly, our solution is to check fairness on the transition relation instead of the calling relation, and propagate the information to determine when it is necessary and sufficient to check for disjunctive well-foundedness on the calling relation. We prove that our approach is sound and complete. We have implemented a prototype of our approach, and confirmed that it is able to automatically verify liveness properties of some non-trivial higher-order programs.

元の言語English
ページ(範囲)57-68
ページ数12
ジャーナルACM SIGPLAN Notices
51
発行部数1
DOI
出版物ステータスPublished - 2016 4 8
外部発表Yes

Fingerprint

Acoustic waves

ASJC Scopus subject areas

  • Computer Science(all)

これを引用

Temporal verification of higher-order functional programs. / Murase, Akihiro; Terauchi, Tachio; Kobayashi, Naoki; Sato, Ryosuke; Unno, Hiroshi.

:: ACM SIGPLAN Notices, 巻 51, 番号 1, 08.04.2016, p. 57-68.

研究成果: Article

Murase, Akihiro ; Terauchi, Tachio ; Kobayashi, Naoki ; Sato, Ryosuke ; Unno, Hiroshi. / Temporal verification of higher-order functional programs. :: ACM SIGPLAN Notices. 2016 ; 巻 51, 番号 1. pp. 57-68.
@article{d2ce1d24a83e498caf8172e9ae99f1b4,
title = "Temporal verification of higher-order functional programs",
abstract = "We present an automated approach to verifying arbitrary omega regular properties of higher-order functional programs. Previous automated methods proposed for this class of programs could only handle safety properties or termination, and our approach is the first to be able to verify arbitrary omega-regular liveness properties. Our approach is automata-theoretic, and extends our recent work on binary-reachability-based approach to automated termination verification of higher-order functional programs to fair termination published in ESOP 2014. In that work, we have shown that checking disjunctive well-foundedness of (the transitive closure of) the {"}calling relation{"} is sound and complete for termination. The extension to fair termination is tricky, however, because the straightforward extension that checks disjunctive well-foundedness of the fair calling relation turns out to be unsound, as we shall show in the paper. Roughly, our solution is to check fairness on the transition relation instead of the calling relation, and propagate the information to determine when it is necessary and sufficient to check for disjunctive well-foundedness on the calling relation. We prove that our approach is sound and complete. We have implemented a prototype of our approach, and confirmed that it is able to automatically verify liveness properties of some non-trivial higher-order programs.",
keywords = "Automata-theoretic verification, Automatic verification, Binary reachability analysis, CEGAR, Higher-order programs, Temporal properties",
author = "Akihiro Murase and Tachio Terauchi and Naoki Kobayashi and Ryosuke Sato and Hiroshi Unno",
year = "2016",
month = "4",
day = "8",
doi = "10.1145/2837614.2837667",
language = "English",
volume = "51",
pages = "57--68",
journal = "SIGPLAN Notices (ACM Special Interest Group on Programming Languages)",
issn = "0362-1340",
publisher = "Association for Computing Machinery (ACM)",
number = "1",

}

TY - JOUR

T1 - Temporal verification of higher-order functional programs

AU - Murase, Akihiro

AU - Terauchi, Tachio

AU - Kobayashi, Naoki

AU - Sato, Ryosuke

AU - Unno, Hiroshi

PY - 2016/4/8

Y1 - 2016/4/8

N2 - We present an automated approach to verifying arbitrary omega regular properties of higher-order functional programs. Previous automated methods proposed for this class of programs could only handle safety properties or termination, and our approach is the first to be able to verify arbitrary omega-regular liveness properties. Our approach is automata-theoretic, and extends our recent work on binary-reachability-based approach to automated termination verification of higher-order functional programs to fair termination published in ESOP 2014. In that work, we have shown that checking disjunctive well-foundedness of (the transitive closure of) the "calling relation" is sound and complete for termination. The extension to fair termination is tricky, however, because the straightforward extension that checks disjunctive well-foundedness of the fair calling relation turns out to be unsound, as we shall show in the paper. Roughly, our solution is to check fairness on the transition relation instead of the calling relation, and propagate the information to determine when it is necessary and sufficient to check for disjunctive well-foundedness on the calling relation. We prove that our approach is sound and complete. We have implemented a prototype of our approach, and confirmed that it is able to automatically verify liveness properties of some non-trivial higher-order programs.

AB - We present an automated approach to verifying arbitrary omega regular properties of higher-order functional programs. Previous automated methods proposed for this class of programs could only handle safety properties or termination, and our approach is the first to be able to verify arbitrary omega-regular liveness properties. Our approach is automata-theoretic, and extends our recent work on binary-reachability-based approach to automated termination verification of higher-order functional programs to fair termination published in ESOP 2014. In that work, we have shown that checking disjunctive well-foundedness of (the transitive closure of) the "calling relation" is sound and complete for termination. The extension to fair termination is tricky, however, because the straightforward extension that checks disjunctive well-foundedness of the fair calling relation turns out to be unsound, as we shall show in the paper. Roughly, our solution is to check fairness on the transition relation instead of the calling relation, and propagate the information to determine when it is necessary and sufficient to check for disjunctive well-foundedness on the calling relation. We prove that our approach is sound and complete. We have implemented a prototype of our approach, and confirmed that it is able to automatically verify liveness properties of some non-trivial higher-order programs.

KW - Automata-theoretic verification

KW - Automatic verification

KW - Binary reachability analysis

KW - CEGAR

KW - Higher-order programs

KW - Temporal properties

UR - http://www.scopus.com/inward/record.url?scp=84965074525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84965074525&partnerID=8YFLogxK

U2 - 10.1145/2837614.2837667

DO - 10.1145/2837614.2837667

M3 - Article

VL - 51

SP - 57

EP - 68

JO - SIGPLAN Notices (ACM Special Interest Group on Programming Languages)

JF - SIGPLAN Notices (ACM Special Interest Group on Programming Languages)

SN - 0362-1340

IS - 1

ER -