On the Church-Rosser property for the direct sum of term rewriting systems
Journal of the ACM (JACM)
Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Handbook of theoretical computer science (vol. B)
Modularity of confluence: a simplified proof
Information Processing Letters
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Modular Aspects of Properties of Term Rewriting Systems Related to Normal Forms
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
On the implementation of construction functions for non-free concrete data types
ESOP'07 Proceedings of the 16th European conference on Programming
Modularity in term rewriting revisited
Theoretical Computer Science
From diagrammatic confluence to modularity
Theoretical Computer Science
| Hi-index | 0.00 |
In [12], Toyama proved that the union of two confluent term-rewriting systems that share absolutely no function symbols or constants is likewise confluent, a property called modularity. The proof of this beautiful modularity result, technically based on slicing terms into an homogeneous cap and a so called alien, possibly heterogeneous substitution, was later substantially simplified in [5,11]. In this paper we present a further simplification of the proof of Toyama's result for confluence, which shows that the crux of the problem lies in two different properties: a cleaning lemma, whose goal is to anticipate the application of collapsing reductions; a modularity property of ordered completion, that allows to pairwise match the caps and alien substitutions of two equivalent terms. We then show that Toyama's modularity result scales up to rewriting modulo equations in all considered cases.