Formalising mathematics in dependent type theory often requires to represent sets as
setoids, ie types with an explicit equality relation. This paper surveys some possible …

A handbook to the Coq software for writing and checking mathematical proofs, with a
practical engineering focus. The technology of mechanized program verification can play a …

A family of syntactic models for the calculus of construction with universes (CC ω) is
described, all of them preserving conversion of the calculus definitionally, and thus giving …

Step-indexed separation logic has proven to be a powerful tool for modular reasoning about
higher-order stateful programs. However, it has only been used to reason about safety …

We give a formalised and machine-checked account of computability theory in the Calculus
of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof …

We present LISA, a proof system and proof assistant for constructing proofs in schematic first-
order logic and axiomatic set theory. The logical kernel of the system is a proof checker for …

Les systèmes communicants mettent en jeu des objets potentiellement infinis (boucles
d'interaction, listes de données infinies, espaces d'états infinis, etc.). L'étude de tels …

This work is about formalizing models of various type theories of the Calculus of
Constructions family. Here we focus on set theoretical models. The long-term goal is to build …

We mechanise the undecidability of various first-order axiom systems in Coq, employing the
synthetic approach to computability underlying the growing Coq Library of Undecidability …

The original motivation1 for the work described in this paper was to determine the proof
theoretic strength of the type theories implemented in the proof development systems Lego …