Type systems for concurrent programs guarantee such desirable properties as communication safety and type refinements facilitate the verification of program invariants. Yet, type-based termination of recursive concurrent programs has been largely unexplored. On the other hand, sized types enable termination checking of functional programs with complex patterns of recursion in the presence of mixed inductive and coinductive types. In this paper, we adapt sized types to the concurrent setting. In particular, we extend a core language for persistent shared memory concurrency based on the semi-axiomatic sequent calculus with recursive types and arithmetic refinements to express size indexing. To prove termination of program reduction, we first define a novel semantic model that reflects persistence in the type system and admits a straightforward generalization to substructural typing. We then develop a compositional validity condition for recursive concurrent programs viewed as circular proofs that guarantees termination.

中文翻译：

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作为过程的圆形证明：通过算术优化的基于类型的终止

用于并发程序的类型系统保证了诸如通讯安全性和类型改进之类的理想属性，从而有助于程序不变性的验证。但是，基本上没有探索基于类型的递归并发程序终止。另一方面，在混合归纳和共归类型存在的情况下，大小类型可以对具有复杂递归模式的功能程序进行终止检查。在本文中，我们将大小类型调整为并发设置。尤其是，我们基于具有半递归类型的顺序演算和递归类型和算术改进来扩展大小索引，从而扩展了用于持久共享内存并发的核心语言。为了证明程序缩减的终止，我们首先定义一个新颖的语义模型，该模型反映类型系统中的持久性，并接受对子结构类型的直接概括。然后，我们为递归并发程序开发一个组合有效性条件，这些条件被视为可保证终止的循环证明。