Cardinalities of Finite Relations in Coq with Applications

Paul Brunet (1, 2) , Damien Pous (1, 2) , Insa Stucke (3)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages
3 Institut für Informatik

In this paper we present an extension of a Coq library for relation algebras and related algebraic structures. So far, the library did not provide any tools about the cardinalities of relations. Thus we add an algebraic axiomatisation of cardinalities. Its point-free nature makes it possible to reason about cardinal purely algebraically, which is well-suited for mechanisation. We present several applications, in the area of graph theory and program verication.

Domaines: Logique en informatique [cs.LO]

Paul Brunet, Damien Pous, Insa Stucke. Cardinalities of Finite Relations in Coq with Applications. Interative Theorem Proving, Aug 2016, Nancy, France. pp.466-474, ⟨10.1007/978-3-319-43144-4_29⟩. ⟨hal-01441262v2⟩