#noindex
The '''λ calculus''' can be called the smallest universal programming language of the world.[* Rojas 파일 첫문장]

'''Lambda calculus''' is an example of a [[reduction_system]] with [[lambda_conversion]] rules constituting its rewrite rules.[* https://mathworld.wolfram.com/ReductionSystem.html 두번째 문단]
([[conversion_rule]] > [[lambda_conversion_rule]] / [[rewriting]] or [[rewriting_rule]] or [[rewrite_rule]])

Sub:

//(tmp) type에 대해: https://en.wikipedia.org/wiki/Lambda_calculus#untypedLambdaCalculus

[[typed_lambda_calculus]]
{
typed lambda calculus

[[타입,type]]있는?

[[수학기초론]]{ WpKo:수학기초론 }에서 [[집합론,set_theory]]의 대안 후보들은 [[Alonzo_Church]]{ '''Alonzo Church''' https://en.wikipedia.org/wiki/Alonzo_Church }의 '''typed lambda-calculus''', Per_Martin-Loef ? { '''Per Martin-Löf''' https://en.wikipedia.org/wiki/Per_Martin-Löf } 의 [[intuitionistic_type_theory]]{ intuitionistic type theory [[WpEn:Intuitionistic_type_theory]] = https://en.wikipedia.org/wiki/Intuitionistic_type_theory WpJa:直観主義型理論 https://plato.stanford.edu/entries/type-theory-intuitionistic/ }가 있다. ([[WpEn:Type_theory]] 처음 부분)

http://foldoc.org/typed+lambda-calculus
[[Wiki:TypedLambdaCalculus]]
[[WpEn:Typed_lambda_calculus]]

"typed lambda calculus"
Ggl:"typed lambda calculus"
}

[[untyped_lambda_calculus]]
[[타입,type]] 없는 [[람다대수,lambda_calculus]].
{
untyped lambda calculus

Twin
https://pub.mearie.org/타입없는람다대수
https://www.pls-lab.org/en/Untyped_lambda_calculus_and_set_theory // [[집합론,set_theory]]
https://www.pls-lab.org/Untyped_lambda_calculus

"untyped lambda calculus"
Ggl:"untyped lambda calculus"
}

[[simply_typed_lambda_calculus]]
{
simply typed lambda calculus

rel. [[simple_type_theory]]
mkl [[untyped_lambda_calculus]]

https://www.pls-lab.org/en/Simply-typed_lambda-calculus
[[WpEn:Simply_typed_lambda_calculus]]

"simply typed lambda calculus"
Ggl:"simply typed lambda calculus"

} // simply typed lambda calculus

[[pure_lambda_calculus]]
{
pure lambda calculus

번역?
순수람다대수?

pure lambda calculus : [[상수,constant]]가 없고 [[함수,function]]만 ... http://foldoc.org/pure+lambda-calculus

"pure lambda calculus"
Ggl:"pure lambda calculus"
}

[[polymorphic_lambda_calculus]] or second-order_lambda_calculus => [[System_F]]
{
'''System F'''
 = polymorphic lambda calculus
 "polymorphic lambda calculus" Ggl:"polymorphic lambda calculus"

'''System F,,ω,,'''
 = higher-order polymorphic lambda calculus
'''System F,,>:,,''' ''이런건 pagename 어떻게? TBD''
 an extension of system F with subtyping. 
WpEn:System_F
[[다형성,polymorphism]]?? curr. [[RR:다형성,polymorphism]]
} // Ggl:"System F"

[[binary_lambda_calculus]]
{
binary lambda calculus

번역?
이진람다대수?

https://esolangs.org/wiki/Binary_lambda_calculus
Google:binary.lambda.calculus
}

----
mklink // 각종 단어/표현/개념들 일단 나열
[[커링,currying]]
{
Haskell Curry의 이름을 땄다고 했나

http://foldoc.org/currying
EoM에서는 https://encyclopediaofmath.org/wiki/Currying redir. to https://encyclopediaofmath.org/wiki/Exponential_law_for_sets
}

익명함수 - [[함수,function]]

람다란?
https://everything2.com/title/lambda

[[,closure]] 와..

변수들 (see [[변수,variable#s-2]])
자유변수 [[free_variable]]
제한변수 [[bound_variable]]
[[자유변수,free_variable]] vs [[bound_variable]] ........ curr at [[변수,variable#s-2]]
 자유변수를 [[치환,substitution]] 연산..?
  치환실례,substitution_instance ?
   {
   "substitution instance"
   Ggl:"substitution instance" Naver:"substitution instance"
   } // substitution instance
[[람다식,lambda_expression]] { [[식,expression]] }

parameter [[parameter]]

[[람다식,lambda_expression]] - [[식,expression]], w rr
{
https://foldoc.org/lambda+expression
... Google:람다식 Google:lambda+expression
}

[[람다항,lambda_term]] - [[항,term]]
{
[[항,term]]
WtEn:lambda_term ? Google:lambda.term
lambda terms에 대해 다음을 할수있..
 적용,application
 [[추상화,abstraction]] - rel. [[람다추상화,lambda_abstraction]]
}

[[람다추상화,lambda_abstraction]] - writing
{
'''lambda abstraction'''
MKL
[[anonymous_function]] 익명함수 무명함수

[[WtEn:lambda_abstraction]] = https://en.wiktionary.org/wiki/lambda_abstraction
 "... It is meant to represent an anonymous function."
http://foldoc.org/lambda+abstraction
https://wiki.haskell.org/Lambda_abstraction
 "A lambda abstraction is another name for an [[anonymous_function]]."
... Google:람다추상화 Google:lambda+abstraction
} // lambda abstraction

[[lambda_lifting]] - w 번역?
{
'''lambda lifting'''
https://foldoc.org/lambda+lifting
WtEn:lambda_lifting x [[Date(2024-01-10T17:27:53)]]
... Google:lambda+lifting Naver:lambda+lifting
}

알파동치 alpha_equivalence
베타축약 beta_reduction
 베타동치,beta_equivalence 베타 동치 beta equivalence
 베타표준형,beta_normal_form 베타 표준형 beta normal form

[[Wiki:AlphaEquivalence]]

α-conversion
β-reduction

= Reduction =
// [[,reduction]] - writing
tmp from [[WpEn:Lambda_calculus#Reduction]]
There are three kinds of reduction:
α-conversion: changing bound variables;
β-reduction: applying functions to their arguments;
η-reduction: which captures a notion of extensionality.
 https://foldoc.org/eta+reduction

https://wiki.haskell.org/Alpha_conversion
 is a renaming of variables.
https://wiki.haskell.org/Eta_conversion
= chk =
||[[항등함수,identity_function]] ||λx.x    ||$x \mapsto x$ ||$\lambda x.x$ ||
||[[상수함수,constant_function]] ||λx.λy.x ||$x \mapsto y$ ||$(\lambda x.y)$ ||
----

= 역사 =
1930년대 Alonzo_Church가

= tmp Files: =
A Tutorial Introduction to the Lambda Calculus, Raul Rojas, FU Berlin
https://personal.utdallas.edu/~gupta/courses/apl/lambda.pdf

https://www3.cs.stonybrook.edu/~cram/cse526/Spring20/Lectures/untyped-lambda.pdf
{ [[Date(2021-07-01T13:07:56)]]에 대충 훑어보기
Church encoding of Booleans, aka Church_booleans - for encoding Booleans in the '''λ-calculus.''' ....이건 표 만들어야됨
Boolean 뿐만 아니라
[[자연수,natural_number]]
[[자료구조,data_structure]]등 각종 ...을 encode.
그 다음 [[평가,evaluation]] - evaluating lambda expressions.
reduction
reduction strategies에 알파 베타 등..
다음 free and bound variables.
α-conversion (renaming)
Y-combinator
Z-combinator
[[재귀함수,recursive_function]]s in the λ-calculus
} (매우대충봄)

= tmp links ko =
https://helloworld.kurly.com/blog/lambda-calculus-1/ 2020
1. lambda expression - 추상화를 하는 방식
2. beta reduction - 추상화된 문제를 풀어내는 방식
3. name clash - beta reduction의 문제
4. alpha conversion - name clash를 방지하기

https://www.sangkon.com/haskell-study-part02/

= mklink Turing =
'''람다계산법'''은 [[튜링_기계,Turing_machine]]와 표현력이 같다. 튜링기계로 돌릴 수 있으면, 람다계산법으로 계산할 수 있고, vice versa.
##(이광근)

= tmp links en =
[[하스켈,Haskell]] wiki 에서
https://wiki.haskell.org/Alpha_conversion
https://wiki.haskell.org/Beta_reduction
https://wiki.haskell.org/Eta_conversion


[[name_capture]] =,name_capture . name_capture
 name capture
 beta_reduction 에서 ...tbw
 http://foldoc.org/name+capture
 Ggl:"name capture"

[[de_Bruijn_notation]] =,de_Bruijn_notation . de_Bruijn_notation
 {
 '''de Bruijn notation'''
 더브라윈_표기법
 [[WtEn:de_Bruijn_notation]] = https://en.wiktionary.org/wiki/de_Bruijn_notation
 lambda_notation 의 일종
 http://foldoc.org/De+Bruijn+notation
 } de Bruijn notation ... Ggl:"de Bruijn notation"

[[lambda_notation]] =,lambda_notation . lambda_notation
 lambda notation
 (not in foldoc!)
 Ggl:"람다 표기"

[[pure_lambda_calculus]] =,pure_lambda_calculus . pure_lambda_calculus
 http://foldoc.org/pure+lambda-calculus

= tmp bmks en =
https://hjaem.info/articles/en_12_2
http://hi.gher.space/wiki/Lambda_calculus

= tmp TODO =
[[RR:람다식,lambda_expression]]

= Misc =
(tmp) (번역에서 쓴 표현에 대해) 여기서 말하는 'calculus'가 해석학의 일종인 미적분학이 아님은 명백하지만, '대수'라는 번역어의 선택은 보통 '대수'↔'algebra'임을 생각해 볼 때 특이한 점. 즉 [[대수학,algebra]]으로 번역한? 람다대수에서 '대수'에 해당하는 것은 see also [[미적분,calculus#s-15]] et [[형식체계,formal_system]]
'''람다계산, 람다계산법, 람다셈법'''도 보인다.
요약하자면 '미적분학'이 아닌 calculus를 마땅히 번역할 단어가 없어서, algebra나 computation에 더 가까운 단어로 번역된 것.

일단 pagename은 가장 자주 쓰이는 '람다대수'로 했는데, calculus를 대수로 번역하기가 좀...(틀린 건 아니지만, 다른 곳에서 다른 뜻으로 많이 쓰임. 대수는 logarithm, algebra 의 번역어로 쓰임. 계산/계산법은 computation/calculation 에 가까운 느낌을 준다. 물론 calculus는, (logarithm은 상관없고) 'algebra', '계산'과 뜻에서 겹치는 부분이 있긴 하나, 아무래도 적당한 번역어가 없는 나머지 이미 다른 곳에서 잘 쓰이는 단어를 임시로 차용한 느낌이다) 

calculus의 번역엔 '논리'도 자주 보인다. 대수/계산(법)/논리 이 셋이 나름 최선의 번역이기는 함 (모두 [[규칙,rule]]/[[논리,logic]]/[[공리,axiom]]/...에 따라 [[식,expression]]/[[문자열,string]]/...(등의 어떤 [[대상,object]])을 변형/rewriting/[[변환,transformation]]/... 등을 하는 [[형식체계,formal_system]]얘기이므로)

calculus의 다른 적당한 번역이 없을까? ... WtEn:calculus KmsE:calculus WpSp:Calculus WpEn:Calculus

= tmp twins =
[[WtEn:lambda_calculus]] = https://en.wiktionary.org/wiki/lambda_calculus

----
Twins:
http://foldoc.org/lambda-calculus
https://pub.mearie.org/람다대수
https://mathworld.wolfram.com/LambdaCalculus.html
http://www.aistudy.co.kr/computer/lambda_calculus.htm
[[WpKo:람다_대수]]
[[WpEn:Lambda_calculus]]
[[WpEn:Category:Lambda_calculus]]
[[Wiki:LambdaCalculus]]
https://plato.stanford.edu/entries/lambda-calculus/
https://everything2.com/title/lambda+calculus
https://ncatlab.org/nlab/show/lambda-calculus

https://esolangs.org/wiki/Lambda_calculus
[[WpSimple:Lambda_calculus]]
https://encyclopediaofmath.org/wiki/Lambda-calculus
https://brilliant.org/wiki/lambda-calculus/

Up:
[[전산학,compsci]]
[[형식체계,formal_system]]
계산모델 ,,computation_model ? ,, Ndict:계산모델  Ggl:계산모델 
[[calculus]] - appropriate pagename? 이 페이지 rename도 고려중.

...Bing:"람다 대수" Ndict:"람다 대수" Ggl:"람다 대수"