We study normalising reduction strategies for infinitary CombinatoryReduction Systems (iCRSs). We prove that all fair, outermost-fair, andneeded-fair strategies are normalising for orthogonal, fully-extended iCRSs.These facts properly generalise a number of results on normalising strategiesin first-order infinitary rewriting and provide the first examples ofnormalising strategies for infinitary lambda calculus.
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