Type-based analysis of logarithmic amortised complexity. (19th June 2022) - Hofmann, Martin; Leutgeb, Lorenz; Obwaller, David; Moser, Georg; Zuleger, Florian
Abstract: 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 potentialbased. 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.