Exporting an Arithmetic Library from Dedukti to HOL

Exporter une librairie d'arithmétique depuis Dedukti vers HOL

François Thiré (1, 2)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 DEDUCTEAM - Deduction modulo, interopérabilité et démonstration automatique

Today, we observe a large diversity of proof systems. This diversity has the negative consequence that a lot of theorems are proved many times. Unlike programming languages, it is difficult for these systems to cooperate because they do not implement the same logic. Logical frameworks are a class of theorems provers that overcome this issue by their capacity of implementing various logics. In this work, we study the STT∀ βδ logic, an extension of the Simple Type Theory that has been encoded in the logical framework Dedukti. We show that this new logic is a good candidate to export proofs to other provers. As an example, we show how this logic has been encoded into Dedukti and how we used it to export proofs to the HOL family provers via OpenTheory.

Mots clés: Dedukti; OpenTheory; HOL; Interoperability; arithmetic

Domaines: Logique en informatique [cs.LO]

François Thiré. Exporting an Arithmetic Library from Dedukti to HOL. 2017. ⟨hal-01668250⟩