From separation logic to first-order logic

  • Authors:

  • Cristiano Calcagno;Philippa Gardner;Matthew Hague

  • Affiliations:

  • Department of Computing, Imperial College, University of London;Department of Computing, Imperial College, University of London;Department of Computing, Imperial College, University of London

  • Venue:
  • FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
  • Year:
  • 2005

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Abstract

Separation logic is a spatial logic for reasoning locally about heap structures. A decidable fragment of its assertion language was presented in [1], based on a bounded model property. We exploit this property to give an encoding of this fragment into a first-order logic containing only the propositional connectives, quantification over the natural numbers and equality. This result is the first translation from Separation Logic into a logic which does not depend on the heap, and provides a direct decision procedure based on well-studied algorithms for first-order logic. Moreover, our translation is compositional in the structure of formulae, whilst previous results involved enumerating either heaps or formulae arising from the bounded model property.