This paper surveys a part of the theory ofβ-reduction inλ-calculus which might aptly be
calledperpetual reductions. The theory is concerned withperpetual reduction strategies, ie …

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 …

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 …

This article extends the termination proof techniques based on reduction orderings to a
higher-order setting, by defining a family of recursive path orderings for terms of a typed …

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 …

For some typedλ-calculi it is easier to prove weak normalization than strong normalization.
Techniques to infer the latter from the former have been invented over the last twenty years …

We present a general methodology of proving the decidability of equational theory of
programming language concepts in the framework of second-order algebraic theories. We …