beta reduction

English

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 ${\\displaystyle (\\lambda x.t)}$ $\text{[math]}$ to a term ${\\displaystyle s}$ $\text{[math]}$ yields an expression ${\\displaystyle t[s/x]}$ $\text{[math]}$ , "t with s instead of x", where all free instances of x in t have been replaced by s.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, 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.

单词	beta reduction
释义	beta reduction English Noun 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 ${\\displaystyle (\\lambda x.t)}$ 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s}$ yields an expression ${\\displaystyle t[s/x]}$ , "t with s instead of x", where all free instances of x in t have been replaced by s. 1996, Roberto DiCosmo; Vincent Danos, The Linear Logic Primer‎, Université de Paris VII, retrieved 2016-04-18, page 43: A natural deduction tree can be put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. Coordinate terms alpha conversion eta conversion
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