Tests and proofs for enumerative combinatorics

Abstract : In this paper we show how the research domain of enumerative combinatorics can benefit from testing and formal verification. We formalize in Coq the combinatorial structures of permutations and maps, and a couple of related operations. Before formally proving soundness theorems about these operations, we first validate them, by using logic programming (Prolog) for bounded exhaustive testing and Coq/QuickChick for random testing. It is an experimental study preparing a more ambitious project about formalization of combinatorial results assisted by verification tools
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Communication dans un congrès
TAP 2016: International Conference on Tests and Proofs, Jul 2016, Vienna, Austria. Springer, Proceedings TAP 2016: International Conference on Tests and Proofs, pp.57-75, 2016, 〈10.1007/978-3-319-41135-4_4〉
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Catherine Dubois, Alain Giorgetti, Richard Genestier. Tests and proofs for enumerative combinatorics. TAP 2016: International Conference on Tests and Proofs, Jul 2016, Vienna, Austria. Springer, Proceedings TAP 2016: International Conference on Tests and Proofs, pp.57-75, 2016, 〈10.1007/978-3-319-41135-4_4〉. 〈hal-01670709〉

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