An Analysis of Permutations in Arrays

This paper is concerned with the synthesis of invariants in programs with arrays. More specifically, we consider properties concerning array contents up to a permutation. For instance, to prove a sorting procedure, one has to show that the result is sorted, but also that it is a permutation of the initial array. In order to analyze this kind of properties, we define an abstract interpretation working on multisets of values, and able to discover invariant; equations about such multisets.