Confluence of Curried Term-Rewriting Systems

Term rewriting systems operate on first-order terms. Presenting such terms in curried form is usually regarded as a trivial change of notation. However, in the absence of a type-discipline, or in the presence of a more powerful type-discipline than simply typed ?-calculus, the change is not as trivial as one might first think. It is shown that currying preserves confluence of em arbitrary/ term rewriting systems. The structure of the proof is similar to Toyama's proof that confluence is a modular property of TRS.