Checking foundational proof certificates for first-order logic

Zakaria Chihani 1 Dale Miller 1 Fabien Renaud 1
1 PARSIFAL - Proof search and reasoning with logic specifications
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : We present the design philosophy of a proof checker based on a notion of foundational proof certificates. At the heart of this design is a semantics of proof evidence that arises from recent advances in the theory of proofs for classical and intuitionistic logic. That semantics is then performed by a (higher-order) logic program: successful performance means that a formal proof of a theorem has been found. We describe how the lambda Prolog programming language provides several features that help guarantee such a soundness claim. Some of these features (such as strong typing, abstract datatypes, and higher-order programming) were features of the ML programming language when it was first proposed as a proof checker for LCF. Other features of lambda Prolog (such as support for bindings, substitution, and backtracking search) turn out to be equally important for describing and checking the proof evidence encoded in proof certificates. Since trusting our proof checker requires trusting a programming language implementation, we discuss various avenues for enhancing one's trust of such a checker.
Type de document :
Communication dans un congrès
PxTP - Proof Exchange for Theorem Proving, Jun 2013, Lake Placid, United States. 2013
Liste complète des métadonnées

Littérature citée [22 références]  Voir  Masquer  Télécharger
Contributeur : Fabien Renaud <>
Soumis le : mardi 19 novembre 2013 - 20:35:58
Dernière modification le : mercredi 14 novembre 2018 - 16:14:01
Document(s) archivé(s) le : jeudi 20 février 2014 - 09:45:47


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-00906486, version 1



Zakaria Chihani, Dale Miller, Fabien Renaud. Checking foundational proof certificates for first-order logic. PxTP - Proof Exchange for Theorem Proving, Jun 2013, Lake Placid, United States. 2013. 〈hal-00906486〉



Consultations de la notice


Téléchargements de fichiers