Type-Based Analysis of Logarithmic Amortised Complexity

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 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.

A cost-aware logical framework

“…Although automated systems such as RaML are without a doubt extremely useful, their scope is limited intentionally to maximize automation. Traditionally, cost bounds in RaML and its cousins range over multivariate polynomials, although support for exponential [Kahn and Hoffmann 2020] and logarithmic [Hofmann et al 2021] potential functions have also been added recently.…”