BI-hyperdoctrines, higher-order separation logic, and abstraction

  • Authors:
  • Bodil Biering;Lars Birkedal;Noah Torp-Smith

  • Affiliations:
  • IT University of Copenhagen, Copenhagen S, Denmark;IT University of Copenhagen, Copenhagen S, Denmark;IT University of Copenhagen, Copenhagen S, Denmark

  • Venue:
  • ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
  • Year:
  • 2007

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Abstract

We present a precise correspondence between separation logic and a simple notion of predicate BI, extending the earlier correspondence given between part of separation logic and propositional BI. Moreover, we introduce the notion of a BI hyperdoctrine, show that it soundly models classical and intuitionistic first- and higher-order predicate BI, and use it to show that we may easily extend separation logic to higher-order. We also demonstrate that this extension is important for program proving, since it provides sound reasoning principles for data abstraction in the presence of aliasing.