Deciding Extensions of the Theories of Vectors and Bags

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.

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