Automated Expected Amortised Cost Analysis of Probabilistic Data Structures

In this paper, we present the first fully-automated expected amortised cost analysis of self-adjusting data structures, that is, randomised splay trees, heaps and meldable heaps, which so far have only (semi-) manually been analysed in literature. Our is stated as a type-and-effect system for first-order functional programming language with support sampling over discrete distributions, non-deterministic choice ticking operator. The latter allows specification fine-grained models. We state two soundness theorems based on different -- but strongly related typing rules ticking, account differently non-terminating computations. Finally provide prototype implementation able to fully automatically analyse aforementioned case studies.