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

7 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
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

Publication series

NameProceedings - Symposium on Logic in Computer Science
ISSN (Print)1043-6871

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)

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