When verifying programs where the data have some recursive structure, it is natural to make use of global invariants that are themselves recursively defined. Though this is mathematically elegant, this makes the proofs more complex, as the preservation of these invariants now requires induction. In particular, this makes the proofs less amenable to automation. An alternative is to use local invariants attached to individual components of the structure and which only involve a bounded number of elements. We call these decentralized invariants. When the structure is updated, the footprint of the modification only impacts a bounded number of invariants and reestablishing them does not require induction. In this paper, we illustrate this idea on three non-trivial programs, for which we achieve fully automated proofs.

在验证数据具有某种递归结构的程序时，自然会利用自己递归定义的全局不变量。尽管从数学上讲这是优雅的，但这使证明更加复杂，因为现在需要归纳这些不变量的保存。特别是，这使证明不适合自动化。一种替代方法是使用局部不变量附加到结构的各个组件上，并且只涉及有限数量的元素。我们称这些分散的不变量。更新结构时，修改的覆盖区仅影响有限数量的不变式，而无需重新建立它们。在本文中，我们在三个非平凡的程序上说明了这一思想，为此我们实现了全自动的证明。