A fixpoint logic and dependent effects for temporal property verification

Yoji Nanjo, Hiroshi Unno, Eric Koskinen, Tachio Terauchi

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

    6 Citations (Scopus)

    Abstract

    Existing approaches to temporal verification of higher-order functional programs have either sacrificed compositionality in favor of achieving automation or vice-versa. In this paper we present a dependent-refinement type & effect system to ensure that well-typed programs satisfy given temporal properties, and also give an algorithmic approach - -based on deductive reasoning over a fixpoint logic - -to typing in this system. The first contribution is a novel type-and-effect system capable of expressing dependent temporal effects, which are fixpoint logic predicates on event sequences and program values, extending beyond the (non-dependent) temporal effects used in recent proposals. Temporal effects facilitate compositional reasoning whereby the temporal behavior of program parts are summarized as effects and combined to form those of the larger parts. As a second contribution, we show that type checking and typability for the type system can be reduced to solving first-order fixpoint logic constraints. Finally, we present a novel deductive system for solving such constraints. The deductive system consists of rules for reasoning via invariants and well-founded relations, and is able to reduce formulas containing both least and greatest fixpoints to predicate-based reasoning.

    Original languageEnglish
    Title of host publicationProceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages759-768
    Number of pages10
    VolumePart F138033
    ISBN (Electronic)9781450355834, 9781450355834
    DOIs
    Publication statusPublished - 2018 Jul 9
    Event33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018 - Oxford, United Kingdom
    Duration: 2018 Jul 92018 Jul 12

    Other

    Other33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018
    CountryUnited Kingdom
    CityOxford
    Period18/7/918/7/12

    Keywords

    • Dependent refinement types
    • Dependent temporal effects
    • Fixpoint logic
    • Higher-order programs
    • Temporal verification

    ASJC Scopus subject areas

    • Software
    • Mathematics(all)

    Fingerprint Dive into the research topics of 'A fixpoint logic and dependent effects for temporal property verification'. Together they form a unique fingerprint.

    Cite this