The Church-rosser theorem in orthogonal combinatory reduction systems

We introduce a notion of Combinatory Reduction Systems (CRSs) by extending the notion of Term Rewriting Systems (TRSs) with variable-binding and substitution mechanisms, define orthogonal CRSs (OCRSs) and prove a strict version of the Church-Rosser theorem for all OCRSs. Our notion of OCRSs is almost equivalent to that of Klop, Kennaway and Van Raamsdonk. Different proofs of the Church-Rosser theorem are in Klop and in Van Raamsdonk.