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Refinement with Time - Refining the Run-Time of Algorithms in Isabelle/HOL

Authors Maximilian P. L. Haslbeck , Peter Lammich

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LIPIcs.ITP.2019.20.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Program verification
  • Theory of computation → Separation logic
  • Theory of computation → Logic and verification
Keywords
  • Isabelle
  • Time Complexity Analysis
  • Separation Logic
  • Program Verification
  • Refinement
  • Run Time
  • Algorithms

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Abstract

Separation Logic with Time Credits is a well established method to formally verify the correctness and run-time of algorithms, which has been applied to various medium-sized use-cases. Refinement is a technique in program verification that makes software projects of larger scale manageable.
Combining these two techniques for the first time, we present a methodology for verifying the functional correctness and the run-time analysis of algorithms in a modular way. We use it to verify Kruskal’s minimum spanning tree algorithm and the Edmonds - Karp algorithm for network flow. 
An adaptation of the Isabelle Refinement Framework [Lammich and Tuerk, 2012] enables us to specify the functional result and the run-time behaviour of abstract algorithms which can be refined to more concrete algorithms. From these, executable imperative code can be synthesized by an extension of the Sepref tool [Lammich, 2015], preserving correctness and the run-time bounds of the abstract algorithm.

Cite As Get BibTex

Maximilian P. L. Haslbeck and Peter Lammich. Refinement with Time - Refining the Run-Time of Algorithms in Isabelle/HOL. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ITP.2019.20

Author Details

Maximilian P. L. Haslbeck
  • Technische Universität München, Germany
Peter Lammich
  • The University of Manchester, England

Funding

  • Haslbeck, Maximilian P. L.: DFG Grant NI 491/16-1
  • Lammich, Peter: DFG Grant LA 3292/1 "Verifizierte Model Checker" and VeTSS grant "Formal Verification of Information Flow Security for Relational Databases"

Acknowledgements

We want to thank Simon Wimmer and Armaël Guéneau, as well as the anonymous reviewers for useful suggestions to improve the paper.

Supplementary Materials

References

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