We introduce a system of monadic affine sized types, which substantially generalizes usual sized types and allows in this way to capture probabilistic higher-order programs that terminate almost surely. Going beyond plain, strong normalization without losing soundness turns out to be a hard task, which cannot be accomplished without a richer, quantitative notion of types, but also without imposing some affinity constraints. The proposed type system is powerful enough to type classic examples of probabilistically terminating programs such as random walks. The way typable programs are proved to be almost surely terminating is based on reducibility but requires a substantial adaptation of the technique.

中文翻译：

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一元仿射大小类型的概率终止

我们引入了一个单子仿射大小类型的系统，它基本上概括了通常大小的类型，并允许以这种方式捕获几乎肯定终止的概率高阶程序。超越简单的强归一化而不失去稳健性被证明是一项艰巨的任务，如果没有更丰富的定量类型概念，而且不施加一些亲和力约束，这是无法完成的。所提出的类型系统足够强大，可以键入概率终止程序的经典示例，例如随机游走。可键入程序被证明几乎肯定会终止的方式是基于可简化性，但需要对该技术进行大量调整。