34 citations
- Laboratoire de Mesure du Carbone 14FR9 papers
- Institut national de recherche en sciences et technologies du numériqueFR5 papers
- Université Paris-SaclayFR5 papers
- Centre National de la Recherche ScientifiqueFR4 papers
- École Normale Supérieure Paris-SaclayFR4 papers
- École PolytechniqueFR4 papers
- Mathématiques et Informatique pour la Complexité et les Systèmes3 papers
- CentraleSupélecFR2 papers
- Centre Inria de SaclayFR2 papers
- Laboratoire d'Informatique de l'École PolytechniqueFR2 papers
- Aix-Marseille UniversitéFR1 paper
- Atos (France)FR1 paper
8 papers · 1 filter
A Complete Proof Synthesis Method for the Cube of Type Systems
Gilles Dowek
We present a complete proof synthesis method for the eight type systems of Barendregt's cube extended with -conversion. Because these systems verify the proofs-as-objects paradi…
A constructive proof of Skolem theorem for constructive logic
Gilles Dowek, Benjamin Werner
If the sequent (Gamma entails forall x exists y A) is provable in first order constructive natural deduction, then the theory (Gamma, forall x (f (x)/y)A), where f is a new functio…
What do we know when we know that a theory is consistent?
Gilles Dowek
Given a first-order theory and a proof that it is consistent, can we design a proof-search method for this theory that fails in finite time when it attempts to prove the formula Fa…
Skolemization in Simple Type Theory: the Logical and the Theoretical Points of View
Gilles Dowek
Peter Andrews has proposed, in 1971, the problem of finding an analog of the Skolem theorem for Simple Type Theory. A first idea lead to a naive rule that worked only for Simple Ty…
A theory independent Curry-De Bruijn-Howard correspondence
Gilles Dowek
Instead of developing a customized typed lambda-calculus for each theory, we attempt to design a general parametric calculus that permits to express the proofs of any theory. This…
Execution traces and reduction sequences
Gilles Dowek
In this note, we defend that the notion of algorithm as a set of execution traces is somewhat independent of the notion of abstract state machine. It can be reformulated in the mor…