This textbook offers a unified, self-contained introduction to the field of term rewriting. Baader
and Nipkow cover all the basic material--abstract reduction systems, termination …

We study higher-order rewrite systems (HRSs) which extend term rewriting to λ-terms. HRSs
can describe computations over terms with bound variables. We show that rewriting with …

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 …

This paper is concerned with the foundations of an extension of pure type systems by
abstract data types, hence the name of Abstract Data Type Systems. ADTS generalize …

In the context of the multiplicity of formal systems, it has become a growing need to express
formal proofs into a common logical framework. This thesis focuses on the use of higher …

This thesis has not been written in isolation; it could not have been. I needed nice people to
be friends with, to chat to, to listen to, to learn from and to become inspired by. I am indebted …

In this paper, we first briefly survey automated termination proof methods for higher-order
calculi. We then concentrate on the higher-order recursive path ordering, for which we …

There are many people that have played an important r^ ole during the research for and the
writing of this thesis. I would like to mention, in no particular order: my friends Marcel and …