Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Termination of term rewriting: interpretation and type elimination
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Explicit Substitutions with de Bruijn's Levels
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Higher-Order Rewriting and Partial Evaluation
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Termination Proofs for Higher-order Rewrite Systems
HOA '93 Selected Papers from the First International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
Comparing Combinatory Reduction Systems and Higher-order Rewrite Systems
HOA '93 Selected Papers from the First International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
Abstract Syntax and Variable Binding
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
The Higher-Order Recursive Path Ordering
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Term rewriting with variable binding: an initial algebra approach
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
An initial algebra approach to term rewriting systems with variable binders
Higher-Order and Symbolic Computation
Higher-order semantic labelling for inductive datatype systems
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
On the relation between sized-types based termination and semantic labelling
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Polymorphic abstract syntax via Grothendieck construction
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Semantic labelling for proving termination of combinatory reduction systems
WFLP'09 Proceedings of the 18th international conference on Functional and Constraint Logic Programming
Multiversal Polymorphic Algebraic Theories: Syntax, Semantics, Translations, and Equational Logic
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We show that the structures of binding algebras and Σ-monoids by Fiore, Plotkin and Turi are sound and complete models of Klop's Combinatory Reduction Systems (CRSs). These algebraic structures play the same role of universal algebra for term rewriting systems. Restricting the algebraic structures to the ones equipped with well-founded relations, we obtain a complete characterisation of terminating CRSs. We can also naturally extend the characterisation to rewriting on meta-terms by using the notion of Σ-monoids.