Collapsing Closures

  • Xuan Li
  • Andy King
  • Lunjin Lu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4079)


A description in the Jacobs and Langen domain is a set of sharing groups where each sharing group is a set of program variables. The presence of a sharing group in a description indicates that all the variables in the group can be bound to terms that contain a common variable. The expressiveness of the domain, alas, is compromised by its intractability. Not only are descriptions potentially exponential in size, but abstract unification is formulated in terms of an operation, called closure under union, that is also exponential. This paper shows how abstract unification can be reformulated so that closures can be collapsed in two senses. Firstly, one closure operation can be folded into another so as to reduce the total number of closures that need to be computed. Secondly, the remaining closures can be applied to smaller descriptions. Therefore, although the operation remains exponential, the overhead of closure calculation is reduced. Experimental evaluation suggests that the cost of analysis can be substantially reduced by collapsing closures.


Logic Program Abstract Interpretation Program Variable Abstract Domain Closure Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xuan Li
    • 1
  • Andy King
    • 2
  • Lunjin Lu
    • 1
  1. 1.Oakland UniversityRochesterUSA
  2. 2.University of KentCanterburyUK

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