Nominal rewriting has been introduced as an extension of first-order term rewriting by a binding mechanism based on the nominal approach. In this paper, we extend Huet’s parallel closure theorem and its generalisation on confluence of left-linear term rewriting systems to the case of nominal rewriting. The proof of the theorem follows a previous inductive confluence proof for orthogonal uniform...

A value-passing, asynchronous process calculus and its associated theory of confluence are considered as a basis for establishing the correctness of distributed algorithms. In particular, we present an asynchronous version of value-passing CCS and we develop its theory of confluence. We show techniques for demonstrating confluence of complex processes in a compositional manner and we study prop...

This paper presents a formalization of decreasing diagrams in the theorem prover Isabelle. It discusses mechanical proofs showing that any locally decreasing abstract rewrite system is confluent. The valley and the conversion version of decreasing diagrams are considered. 1998 ACM Subject Classification F.3.1, F.4.2

The decreasing diagrams technique is a complete method to reduce confluence of a rewrite relation to local confluence. Whereas previous presentations have focussed on the proof the technique is correct, here we focus on applicability. We present a simple but powerful generalisation of the technique, requiring peaks to be closed only by conversions instead of valleys, which is demonstrated to fu...