Towards Formalization and Sharing of Atelier B Proofs with Dedukti

Claude Stolze (1, 2, 3) , Olivier Hermant (4, 3) , Romain Guillaumé (4)

1 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay
2 LMF - Laboratoire Méthodes Formelles
3 DEDUCTEAM - Deduction modulo, interopérabilité et démonstration automatique
4 CRI - Centre de Recherche en Informatique

Atelier B is widely used to develop safe-by-construction programs. Numerous systems and pieces of software have been designed and built at the highest level of safety with this framework. But similar toolsets are used for the same purpose, and we advocate that they would all benefit from proof-exchange facilities. To this aim, we introduce an export tool of Atelier B proof obligations to Dedukti, a universal logical framework based on type theory, and designed for interoperability. We then describe a preliminary experimentation to reconstruct detailed demonstrations of those proof obligations, so that they can be doublechecked by Dedukti, and be ready for a later export to the other tools. We also discuss the methodologies and potential framework architectures that could be helpful in such a proof-exchange objective.

Keywords: B Method; Type theory; Automated reasoning; Proof theory; Formal methods; Set theory; Interoperability

Domains: Computer Science [cs]

Claude Stolze, Olivier Hermant, Romain Guillaumé. Towards Formalization and Sharing of Atelier B Proofs with Dedukti. 2024. ⟨hal-04398119⟩