Confluence and Termination of Simply Typed Term Rewriting Systems
We propose simply typed term rewriting systems (STTRSs), which extend first-order rewriting by allowing higher-order functions. We study a simple proof method for con uence which employs a characterization of the diamond property of a parallel reduction. By an application of the proof method, we obtain a new con uence result for orthogonal conditional STTRSs. We also discuss a semantic method for proving termination of STTRSs based on monotone interpretation.
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