beta reduction

English

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Noun

beta reduction (countable and uncountable, plural beta reductions)

1. The act of beta reducing, an instance of replacing a function call by the result of calling a function.
2. (computing theory) One of the three rewrite rules of the lambda calculus, which states that the application of a lambda abstraction ${\displaystyle (\lambda x.t)}$ to a term ${\displaystyle s}$ yields an expression ${\displaystyle t[s/x]}$, "t with s instead of x", where all free instances of x in t have been replaced by s.
   • 1996, Roberto DiCosmo with Vincent Danos, The Linear Logic Primer‎, Université de Paris VII, retrieved 18 April 2016, page 43:

     A natural deduction tree can be put in exact correspondence with typed λ-calculus (that can be considered as just a notation for such deductions), and the cut-elimination in Natural Deduction corresponds exactly to β-reduction in λ-calculus.

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