eta expansion - meaning and definition. What is eta expansion
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What (who) is eta expansion - definition

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

eta expansion         
Eta Hentz         
HUNGARIAN-BORN FASHION DESIGNER
Madame Eta
Eta Valer Hentz (1895–1986) was a Hungarian-American fashion designer active in the US from the 1920s to the 1940s. Mainly known as Madame Eta, she was particularly known for flattering ready-to-wear clothing inspired by Ancient Greece and the Middle Ages.
Laplace expansion         
N×N DETERMINANT AS SUM OF N MINORS WEIGHTED BY COFACTOR FROM ROW AND COLUMN NOT IN MINOR
Determinant expansion; Expansion by minors; Cofactor expansion
In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression of the determinant of an matrix as a weighted sum of minors, which are the determinants of some submatrices of . Specifically, for every ,

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.