We introduce a novel amortised resource analysis couched in a type-and-effect system. Our analysis is formulated in terms of the physicist's method of amortised analysis, and is potential-based. The type system makes use of logarithmic potential functions and is the first such system to exhibit *logarithmic amortised complexity*. With our approach we target the automated analysis of self-adjusting data structures, like splay trees, which so far have only manually been analysed in the literature. In particular, we have implemented a semi-automated prototype, which successfully analyses the zig-zig case of *splaying*, once the type annotations are fixed.

中文翻译：

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基于类型的对数摊销复杂度分析

我们介绍了一种基于类型和效果系统的新型摊销资源分析。我们的分析是根据物理学家的摊销分析方法制定的，并且是基于势能的。类型系统利用对数势函数，并且是第一个显示“对数摊余复杂度”的系统。通过我们的方法，我们的目标是对自动调整的数据结构（例如八叉树）进行自动分析，到目前为止，文献中仅对它们进行了手动分析。特别是，我们实现了一个半自动化的原型，一旦类型注释固定，该原型就可以成功分析* splaying *的之字形情况。