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In mathematical logic, the Church-Rosser theorem states that, in the lambda calculus,
a term has at most one normal form. More formally, the Church-Rosser property states that the simply typed lambda calculus without <math>\eta<math>-reduction is confluent.
Specifically, if two different reductions of a term both terminate in normal forms, then the two normal forms will be identical. It is the Church-Rosser theorem that justifies references to "the normal form" of a certain term. This property is also known more generally as confluence.
The theorem was proved in 1937 by Alonzo Church and J. Barkley Rosser.
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