Talk:S and K Turing-completeness proof

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This article aims to show that S and K combinators are Turing-complete but only shows a way to convert a lambda expression into combinators. Can someone explain why this is already enough? Why is there no need for prooving the equivalence of the reduction rules and that the reduced expression can be translated back into lambda calculus resulting in an equally simple expression as direct reduction in lambda calculus would give? --(this comment by at 20:09, 27 March 2013‎ UTC; please sign your comments with ~~~~)

You have a point there. For now, I added a short note about it. --Ørjan (talk) 23:24, 27 March 2013 (UTC)