The Correctness of Set-Sharing

  • Patricia M. Hill
  • Roberto Bagnara
  • Enea Zaffanella
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1503)


It is important that practical data flow analysers are backed by reliably proven theoretical results. Abstract interpretation provides a sound mathematical framework and necessary generic properties for an abstract domain to be well-defined and sound with respect to the concrete semantics. In logic programming, the abstract domain Sharing is a standard choice for sharing analysis for both practical work and further theoretical study. In spite of this, we found that there were no satisfactory proofs for the key properties of commutativity and idempotence that are essential for Sharing to be well-defined and that published statements of the safeness property assumed the occur-check. This paper provides a generalisation of the abstraction function for Sharing that can be applied to any language, with or without the occur-check. The results for safeness, idempotence and commutativity for abstract unification using this abstraction function are given.


abstract interpretation logic programming occur-check rationaltrees set-sharing 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Patricia M. Hill
    • 1
  • Roberto Bagnara
    • 2
  • Enea Zaffanella
    • 3
  1. 1.School of Computer StudiesUniversity of LeedsLeedsUK
  2. 2.Dipartimento di MatematicaUniversità degli Studi di ParmaItaly
  3. 3.Servizio IX AutomazioneUniversità degli Studi di ModenaItaly

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