beta reduction - definizione. Che cos'è beta reduction
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Cosa (chi) è beta reduction - definizione

FORMAL SYSTEM IN MATHEMATICAL LOGIC
Lamda calculus; Lambda-calculus; Lambda abstraction; Lambda-definable function; Lambda-definable functions; Lambda calculas; Beta reduction; Alpha conversion; Lambda-recursive function; Lambda programming; Eta reduction; Lambda Calculus; Untyped lambda calculus; Λ-calculus; Alpha equivalence; Eta expansion; Abstraction operator; Alpha reduction; Beta substitution; Beta conversion; Α conversion; Λ calculus; Β-reduction; B-reduction; L-calculus; L calculus; A conversion; Beta-reduction; Λa-calculus; Lanbda-calculus; Lambda kalkül; Alpha renaming; Lambda calculi; Λ-abstraction; AlphaRenaming; Α-conversion; Capture-avoiding substitution; Lambda term; Lamda expression; Alpha-renaming; Alpha-conversion; Eta conversion; Eta-conversion; Η-conversion; Η conversion; Lambda language; Type-free lambda calculus; Typefree lambda calculus; Type free lambda calculus; Eta-reduction; Functional abstraction; Λx; Λy; Λz; Anonymous function abstraction; Lambda-calculi; Lambda-term bound variables; Lambda terms; Alpha equivalent

beta reduction         
[lambda-calculus] The application of a {lambda abstraction} to an argument expression. A copy of the body of the lambda abstraction is made and occurrences of the {bound variable} being replaced by the argument. E.g. ( x . x+1) 4 --> 4+1 Beta reduction is the only kind of reduction in the {pure lambda-calculus}. The opposite of beta reduction is {beta abstraction}. These are the two kinds of beta conversion. See also name capture.
Dimensionality reduction         
  • A visual depiction of the resulting LDA projection for a set of 2D points.
  • A visual depiction of the resulting PCA projection for a set of 2D points.
PROCESS OF REDUCING THE NUMBER OF RANDOM VARIABLES UNDER CONSIDERATION
Dimension reduction; Dimensionality Reduction; Dimensionality reduction algorithm; Linear dimensionality reduction
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable (hard to control or deal with).
Great Reduction         
LAND REFORMS IN SECOND MILLENNIUM SWEDEN; A TAKING-BACK OF POSSESSIONS FROM THE NOBILITY BY THE CROWN
Great Reduction (Sweden); Reduction (Sweden)
In the Great Reduction of 1680, by which the ancient landed nobility lost its power base, the Swedish Crown recaptured lands earlier granted to the nobility. Reductions () in Sweden and its dominions were the return to the Crown of fiefs that had been granted to the Swedish nobility.

Wikipedia

Lambda calculus

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics.

Lambda calculus consists of constructing lambda terms and performing reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules:

  • x {\displaystyle x} – variable, a character or string representing a parameter or mathematical/logical value.
  • ( λ x . M ) {\textstyle (\lambda x.M)} – abstraction, function definition ( M {\textstyle M} is a lambda term). The variable x {\textstyle x} becomes bound in the expression.
  • ( M   N ) {\displaystyle (M\ N)} – application, applying a function M {\textstyle M} to an argument N {\textstyle N} . Both M {\textstyle M} and N {\textstyle N} are lambda terms.

The reduction operations include:

  • ( λ x . M [ x ] ) ( λ y . M [ y ] ) {\textstyle (\lambda x.M[x])\rightarrow (\lambda y.M[y])} – α-conversion, renaming the bound variables in the expression. Used to avoid name collisions.
  • ( ( λ x . M )   E ) ( M [ x := E ] ) {\textstyle ((\lambda x.M)\ E)\rightarrow (M[x:=E])} – β-reduction, replacing the bound variables with the argument expression in the body of the abstraction.

If De Bruijn indexing is used, then α-conversion is no longer required as there will be no name collisions. If repeated application of the reduction steps eventually terminates, then by the Church–Rosser theorem it will produce a β-normal form.

Variable names are not needed if using a universal lambda function, such as Iota and Jot, which can create any function behavior by calling it on itself in various combinations.