Tests and proofs for enumerative combinatorics

Catherine Dubois (1, 2, 3) , Alain Giorgetti (4) , Richard Genestier (4)

1 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
2 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
3 CNRS - Centre National de la Recherche Scientifique
4 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

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

Mots clés: Random Testing; Exhaustive Testing; Enumerative Combinatorics; Boolean Function; Logic Programming

Domaines: Mathématique discrète [cs.DM]

Catherine Dubois, Alain Giorgetti, Richard Genestier. Tests and proofs for enumerative combinatorics. TAP 2016: International Conference on Tests and Proofs, Jul 2016, Vienna, Austria. pp.57-75, ⟨10.1007/978-3-319-41135-4_4⟩. ⟨hal-01670709⟩