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What is CHURCH-ROSSER THEOREM? What does CHURCH-ROSSER THEOREM mean? CHURCH-ROSSER THEOREM meaning

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✪✪✪✪✪ http://www.theaudiopedia.com ✪✪✪✪✪ What is CHURCH-ROSSER THEOREM? What does CHURCH-ROSSER THEOREM mean? CHURCH-ROSSER THEOREM meaning - CHURCH-ROSSER THEOREM definition - CHURCH-ROSSER THEOREM explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license. SUBSCRIBE to our Google Earth flights channel - https://www.youtube.com/channel/UC6UuCPh7GrXznZi0Hz2YQnQ In mathematics and theoretical computer science, the Church–Rosser theorem states that, when applying reduction rules to terms in the lambda calculus, the ordering in which the reductions are chosen does not make a difference to the eventual result. More precisely, if there are two distinct reductions or sequences of reductions that can be applied to the same term, then

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What is CHURCH-ROSSER THEOREM? What does CHURCH-ROSSER THEOREM mean? CHURCH-ROSSER THEOREM meaning - CHURCH-ROSSER THEOREM definition - CHURCH-ROSSER THEOREM explanation.



Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.



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In mathematics and theoretical computer science, the Church–Rosser theorem states that, when applying reduction rules to terms in the lambda calculus, the ordering in which the reductions are chosen does not make a difference to the eventual result. More precisely, if there are two distinct reductions or sequences of reductions that can be applied to the same term, then there exists a term that is reachable from both results, by applying (possibly empty) sequences of additional reductions. The theorem was proved in 1936 by Alonzo Church and J. Barkley Rosser, after whom it is named.



The theorem is symbolized by the diagram at right: if term a can be reduced to both b and c, then there must be a further term d (possibly equal to either b or c) to which both b and c can be reduced. Viewing the lambda calculus as an abstract rewriting system, the Church–Rosser theorem states that the reduction rules of the lambda calculus are confluent. As a consequence of the theorem, a term in the lambda calculus has at most one normal form, justifying reference to "the normal form" of a given normalizable term.



The Church–Rosser theorem also holds for many variants of the lambda calculus, such as the simply-typed lambda calculus, many calculi with advanced type systems, and Gordon Plotkin's beta-value calculus. Plotkin also used a Church–Rosser theorem to prove that the evaluation of functional programs (for both lazy evaluation and eager evaluation) is a function from programs to values (a subset of the lambda terms).



In older research papers, a rewriting system is said to be Church–Rosser, or to have the Church–Rosser property, when it is confluent.
Barkley Rosser
I remember how loud it was. I was a young Economics undergraduate, and most professors didn’t really slam points home the way Dr. Rosser did. He would bang on the table and throw things around the classroom. Not for the faint of heart, but he definitely kept my attention and made me smile. It is hard to not smile around J. Barkley Rosser, especially when he gets going on economic theory. The passion comes through and encourages you to come along with it in a truly contagious way. After meeting him, it is as if you can just tell that anybody who knows that much and has that much to say deserves your attention.

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