Deciding Extensions of the Theories of Vectors and Bags

  • Patrick Maier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5403)


Vectors and bags are basic collection data structures, which are used frequently in programs and specifications. Reasoning about these data structures is supported by established algorithms for deciding ground satisfiability in the theories of arrays (for vectors) and multisets (for bags), respectively. Yet, these decision procedures are only able to reason about vectors and bags in isolation, not about their combination.

This paper presents a decision procedure for the combination of the theories of vectors and bags, even when extended with a function bagof bridging between vectors and bags. The function bagof converts vectors into the bags of their elements, thus admitting vector/bag comparisons. Moreover, for certain syntactically restricted classes of ground formulae decidability is retained if the theory of vectors is extended further with a map function which applies uninterpreted functions to all elements of a vector.


Decision Procedure Function Symbol Disjunctive Normal Form Presburger Arithmetic Uninterpreted Function 
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 2008

Authors and Affiliations

  • Patrick Maier
    • 1
  1. 1.Laboratory for Foundations of Computer Science School of InformaticsThe University of EdinburghScotland

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