Machine-Checked Verification of the Correctness and Amortized Complexity of an Efficient Union-Find Implementation

  • Arthur Charguéraud
  • François Pottier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9236)


Union-Find is a famous example of a simple data structure whose amortized asymptotic time complexity analysis is non-trivial. We present a Coq formalization of this analysis. Moreover, we implement Union-Find as an OCaml library and formally endow it with a modular specification that offers a full functional correctness guarantee as well as an amortized complexity bound. Reasoning in Coq about imperative OCaml code relies on the CFML tool, which is based on characteristic formulae and Separation Logic, and which we extend with time credits. Although it was known in principle that amortized analysis can be explained in terms of time credits and that time credits can be viewed as resources in Separation Logic, we believe our work is the first practical demonstration of this approach.


Function Call Garbage Collection Separation Logic Functional Correctness Characteristic Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Inria and LRIUniversité Paris Sud, CNRSOrsayFrance
  2. 2.InriaParis-RocquencourtFrance

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