Temporal verification of higher-order functional programs

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Citations (Scopus)


We present an automated approach to verifying arbitrary omegaregular 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.

Original languageEnglish
Title of host publicationPOPL 2016 - Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
EditorsRupak Majumdar, Rastislav Bodik
PublisherAssociation for Computing Machinery
Number of pages12
ISBN (Electronic)9781450335492
Publication statusPublished - 2016 Jan 11
Externally publishedYes
Event43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2016 - St. Petersburg, United States
Duration: 2016 Jan 202016 Jan 22

Publication series

NameConference Record of the Annual ACM Symposium on Principles of Programming Languages
ISSN (Print)0730-8566


Other43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2016
Country/TerritoryUnited States
CitySt. Petersburg


  • Automata-theoretic verification
  • Automatic verification
  • Binary reachability analysis
  • Higher-order programs
  • Temporal properties

ASJC Scopus subject areas

  • Software


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