beta reduction
English[edit]
Noun[edit]
beta reduction (plural beta reductions)
 The act of beta reducing, an instance of replacing a function call by the result of calling a function.
 (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a lambda abstraction to a term yields an expression , "t with s instead of x", where all free instances of x in t have been replaced by s.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 December 14, Roberto DiCosmo; Vincent Danos, The Linear Logic Primer^{[1]}, Université de Paris VII, retrieved 20160418, page 43:
 A natural deduction tree can be put in exact correspondence with typed λcalculus (that can be considered as just a notation for such deductions), and the cutelimination in Natural Deduction corresponds exactly to βreduction in λcalculus.
