beta reduction

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beta reduction (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a lambda abstraction to a term yields an expression , "t with s instead of x", where all free instances of x in t have been replaced by s.
    • 1996, Roberto DiCosmo; Vincent Danos, The Linear Logic Primer[1], Université de Paris VII, retrieved 2016-04-18, 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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