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A lightweight approach to nontermination inference using Constrained Horn Clauses

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Abstract

Nontermination is an unwanted program property for some software systems, and a safety property for other systems. In either case, automated discovery of preconditions for nontermination is of interest. We introduce NtHorn, a fast lightweight nontermination analyser, which is able to deduce non-trivial sufficient conditions for nontermination. Using Constrained Horn Clauses (CHCs) as a vehicle, we show how established techniques for CHC program transformation and abstract interpretation can be exploited for the purpose of nontermination analysis. NtHorn is comparable in effectiveness to the state-of-the-art nontermination analysis tools, as measured on standard competition benchmark suites (consisting of integer manipulating programs), while typically solving problems faster by one order of magnitude.

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Notes

  1. A comma to the right of the arrow in a CHC denotes conjunction, and conjunction binds tighter than the arrow.

  2. We use \(\forall (\varphi )\) for the universal closure of formula \(\varphi \), that is, \(\forall V (\varphi )\), where V is the set of free variables in \(\varphi \).

  3. Readers familiar with predicative programming a la Hehner [38], may prefer to rename \(\texttt{d}\) in \(c_1\) to \(\texttt{a}'\) (and similarly rewrite other clauses), to support the reading “value of \(\texttt{a}\) after the assignment”.

  4. Available from https://github.com/bishoksan/NtHorn.git.

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Acknowledgements

We thank John Gallagher and the anonymous reviewers for their insightful comments, which led to many improvements. Bishoksan Kafle has been partially funded by the Spanish Ministry of Research, Science and Innovation, grant MICINN PID2019-108528RB-C21 ProCode and Madrid P2018/TCS-4339 BLOQUES-CM. Peter Stuckey’s work was supported by the Australian Research Council OPTIMA ITTC, Project ID IC200100009.

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  1. IMDEA Software Institute, IMDEA, Madrid, Spain

    Bishoksan Kafle

  2. Computing and Information Systems, The University of Melbourne, Melbourne, 3010, VIC, Australia

    Graeme Gange, Peter Schachte & Harald Søndergaard

  3. Faculty of IT, Monash University, Clayton, 3800, VIC, Australia

    Peter J. Stuckey

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Kafle, B., Gange, G., Schachte, P. et al. A lightweight approach to nontermination inference using Constrained Horn Clauses. Softw Syst Model 23, 319–342 (2024). https://doi.org/10.1007/s10270-024-01161-5

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