Tests and Proofs for Enumerative Combinatorics
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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