We set out to study the consequences of the assumption of types of wellfounded trees in
dependent type theories. We do so by investigating the categorical notion of wellfounded …

This paper extends the termination proof techniques based on reduction orderings to a
higher-order setting, by adapting the recursive path ordering definition to terms of a typed …

This paper presents general syntactic conditions ensuring the strong normalisation and the
logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus …

In a previous work (“Abstract Data Type Systems”, TCS 173 (2), 1997), the last two authors
presented a combined language made of a (strongly normalizing) algebraic rewrite system …

Automatic proof checking is about using a computer to check the validity of proofs of
mathematical statements. Since this verification is purely computational, it offers a high …

Given the different perspectives from which a complex software system has to be analyzed,
the multiplicity of formalisms is unavoidable. This poses two important technical challenges …

A constructive proof of the Gödel-Rosser incompleteness theorem [9] has been completed
using Coq proof assistant. Some theory of classical first-order logic over an arbitrary …

This paper presents a method to translate a proof in an extensional version of the Calculus
of Constructions into a proof in the Calculus of Inductive Constructions extended with a few …

For the most part, rewriting techniques have been developed and applied to support efficient
equational reasoning and equational specification, verification, and programming …

In the last twenty years, several approaches to higher-order rewriting have been proposed,
among which Klop's Combinatory Rewrite Systems (CRSs), Nipkow's Higher-order Rewrite …