Combinatory reduction systems, or CRSs for short, were designed to combine the usual first-
order format of term rewriting with the presence of bound variables as in pure λ-calculus and …

Nominal rewriting is based on the observation that if we add support for α-equivalence to
first-order syntax using the nominal-set approach, then systems with binding, including …

In the absence of termination, confluence of rewriting systems is often hard to establish. The
class of orthogonal rewriting systems is the main class of not-necessarily-terminating, but …

Calculi with explicit substitutions (ES) are widely used in different areas of computer science.
Complex systems with ES were developed these last 15 years to capture the good …

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 this paper two formats of higher-order rewriting are compared: Combinatory Reduction
Systems introduced by Klop and Higher-order Rewrite Systems defined by Nipkow …

We present a generalisation of first-order rewriting which allows us to deal with terms
involving binding operations in an elegant and practical way. We use a nominal approach to …

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 …

In this paper, we show how to extend the notion of reducibility introduced by Girard for
proving the termination of β-reduction in the polymorphic λ-calculus, to prove the termination …

The class of orthogonal rewriting systems (rewriting systems where rewrite steps cannot
depend on one another) is the main class of not-necessarily-terminating rewriting systems …