Hydras & Co.: Formalized mathematics in Coq for inspiration and entertainment

Pierre Castéran (1, 2) , Jérémy Damour (3) , Karl Palmskog (4) , Clément Pit-Claudel (5) , Théo Zimmermann (6, 3)

1 UB - Université de Bordeaux
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 PI.R2 - Design, study and implementation of languages for proofs and programs
4 KTH - KTH Royal Institute of Technology [Stockholm]
5 MIT CSAIL - MIT Computer Science & Artificial Intelligence Lab
6 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

Hydras & Co. is a collaborative library of discrete mathematics for the Coq proof assistant, developed as part of the Coq-community organization on GitHub. The Coq code is accompanied by an electronic book, generated with the help of the Alectryon literate proving tool. We present the evolution of the mathematical contents of the library since former presentations at JFLA meetings. Then, we describe how the structure of the project is determined by two requirements which must be continuously satisfied. First, the Coq code needs to be compatible with its ever-evolving dependencies (the Coq proof assistant and several Coq packages both from inside and outside Coq-community) and reverse dependencies (Coq-community projects that depend on it). Second, the book needs to be consistent with the Coq code, which undergoes frequent changes to improve structure and include new material. We believe Hydras & Co. demonstrates that books on formalized mathematics are not limited to providing exposition of theories and reasoning techniquesthey can also provide inspiration and entertainment that transcends educational goals.

Domaines: Logique en informatique [cs.LO]

Pierre Castéran, Jérémy Damour, Karl Palmskog, Clément Pit-Claudel, Théo Zimmermann. Hydras & Co.: Formalized mathematics in Coq for inspiration and entertainment. Journées Francophones des Langages Applicatifs: JFLA 2022, Jun 2022, St-Médard d'Excideuil, France. ⟨hal-03404668v2⟩