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 …

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 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 …

The Functional Machine Calculus (FMC), recently introduced by the authors, is a
generalization of the lambda-calculus which may faithfully encode the effects of higher-order …

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 …

Term rewriting systems play an important role in many areas of computer science. In
essence, they provide an abstract way to define algorithms. The theory is simple: terms …

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 …

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 …