#noindex
식은 [[수,number]]와 [[변수,variable]]들을 [[연산,operation]]으로 연결한다.[* https://brilliant.org/courses/pre-algebra/variables/day-2-expressions/2/ An expression connects numbers and variables with operations such as addition, subtraction, multiplication, and division.]

식은 [[평가,evaluation]]의 대상?
 이 때 [[대입,assignment]]이 일어남?
복잡한 식은 [[단순화,simplification]]의 대상.

식을 [[평가,evaluation]]한다는 것은, 그 [[값,value]]을 찾는 것. [[변수,variable]]에 [[대입,assignment]]을 한다던지.
 chk 평가의 과정 중에서 [[식,expression]]의 구성요소들에 대한 [[연산,operation]]이 일어남?
----
Cmp
[[formula]] { [[논리식,logical_formula]] [[논리식,logic_formula]] [[논리식,formula]]  REL: [[원자식,atom]](atomic_formula) [[명제식,propositional_formula]]  .... }
well-formed_formula - [[적형식,wff]]

----
MKL
[[문자열,string]]
[[텀,term]] = [[항,term]]
[[상수,constant]]
[[연결사,connective]]
[[괄호,gwalho]]

MKL/MKCLEAR
[[명제,proposition]]
[[명제식,propositional_formula]]
[[포뮬러,formula]]
[[논리식,logical_formula]] = [[논리식,logic_formula]] ~= [[적형식,wff]]
[[연산자,operator]] [[연산,operation]] and [[피연산자,operand]](ex [[수,number]] [[상수,constant]] [[변수,variable]] ...) 이것들을 [[연결,connection]] ...
[[문장,sentence]]

----
Sub:

mathematical expression 수식
[[수식,mathematical_expression]] ?
수식
mathematical_expression - 현재 this page와 구분을 두고 있지는 않은데 나중에 분리?
//한다면 [[수식,mathematical_expression]]
{

WtEn:mathematical_expression ???? qqqqqqqqqiiiiiiii

rel. [[표기법,notation]] > 수학적표기법 [[mathematical_notation]]
{
수학적표기법

Ggl:수학적표기법

[[Wiki:MathematicalNotation]]
= http://wiki.c2.com/?MathematicalNotation
} // 수학적표기법 

} // 수식

[[대수식,algebraic_expression]] =대수식,algebraic_expression =,algebraic_expression 대수식 algebraic_expression
algebraic expression
Ggl:"algebraic expression"
대수식 via KmsE:"algebraic expression"
via [[리듀스,Reduce]]매뉴얼

[[불_식,Boolean_expression]]

[[람다식,lambda_expression]]

[[well-defined_expression]] - [[well-definedness]] - curr at [[정의,definition?action=highlight&value=well-defined_expression]]

[[symbolic_expression]] =,symbolic_expression =,symbolic_expression . symbolic_expression
{
symbolic expression
기호식 ? 심볼식 심벌식 ?

이것은 좁게는 Lisp의 s-expression = sexp 를 뜻하는 경우도 있고, 넓게는 symbolic_computation 이 가능한 그 (정확히 tbw)...

[[WtEn:symbolic_expression]] = https://en.wiktionary.org/wiki/symbolic_expression
 여기선 sexp와 동의어로 나옴. [[Date(2023-11-22T13:06:58)]] 근데 항상 그런가? 에 대한 대답은 No.

WpEn:Symbolic_expression = https://en.wikipedia.org/wiki/Symbolic_expression
 [[Date(2023-11-22T13:06:58)]] redir to :
 https://en.wikipedia.org/wiki/Expression#Symbolic

...
"symbolic expression"
Ndict:"symbolic expression"
Ggl:"symbolic expression"

Up: symbol( [[심벌,symbol]] [[기호,symbol]] .. ) [[식,expression]]
} // symbolic expression

[[s-expression]] =,s-expression =,s-expression . s-expression
{
[[s식,s-expression]]이 최선의 pagename??
작성중인곳은 [[S식,S-expression]]라고 써놓았긴 한데 capitalization을 할지 말지 TBD
 [[Date(2023-11-07T09:32:14)]] ... wpen 보면 capitalize하는 게 맞는 것 같다
=s식,s-expression =,s-expression =,sexp .
=S식,S-expression =,s-expression =,sexp . s-expression sexp
'''S-expression, s-expr, sexpr, sexp'''.
S는 'symbolic'에서. // ([[심벌,symbo]] [[심볼,symbol]] [[기호,symbol]] [[symbolic]]...중?)
p SExpression
MKL
[[리스프,Lisp]]
[[트리,tree]]
[[리스트,list]]
[[John_McCarthy]]
Cmp [[m-expression]] [[M식,M-expression]] //바로아래section

code와 data 둘다 표현
 이거 분명 [[,homoiconicity]] ... 같은건지 아님 관련인지 chk

Sub:
[[canonical_S-expression]] =,canonical_S-expression =,canonical_S-expression . canonical_S-expression |=,csexp csexp
{
canonical s-expression

[[WpEn:Canonical_S-expressions]] = https://en.wikipedia.org/wiki/Canonical_S-expressions
 "and maximizing the speed of parsing."

https://en.wiktionary.org/wiki/canonical_S-expression

https://en.wiktionary.org/wiki/csexp x [[Date(2023-11-07T09:36:31)]]

"canonical S-expression"
Ggl:"canonical S-expression"

} // canonical S-expression

----
Twins:
[[WpKo:S-표현식]] = https://ko.wikipedia.org/wiki/S-표현식
[[WpEn:S-expression]] = https://en.wikipedia.org/wiki/S-expression
[[WpJa:S式]] = https://ja.wikipedia.org/wiki/S式
[[Wiki:EssExpressions]] = http://wiki.c2.com/?EssExpressions

Up: [[data_serialization_format]] [[식,expression]] [[표기법,notation]]?

Ggl:s-expression
Bing:s-expression
Ndict:s-expression
Naver:s-expression

} // s-exp

m-expression
M-expression 이것도
[[M식,M-expression]]으로 할지 (w)
[[m식,m-expression]]으로 할지 + 뒤에 ,mexp 를 붙일지, TBD
=M식,M-expression =,m-expression =,mexp . m-expression mexp
{
'''meta-expression'''. M은 'meta'에서.
mklink: [[John_McCarthy]]
[[WpEn:M-expression]] = https://en.wikipedia.org/wiki/M-expression
[[Wiki:EmExpressions]] = https://wiki.c2.com/?EmExpressions
Up: [[식,expression]] [[표기법,notation]]?
}


[[let_expression]] =,let_expression . let_expression
{
let expression

두 형태: let or let rec. "[[let_rec]] is an extension of the simple '''let expression''' which uses the [[fixed-point_combinator]] to implement [[재귀,recursion]]." (we)

rel
[[람다추상화,lambda_abstraction]]
[[scope]]

------
WtEn:let_expression = https://en.wiktionary.org/wiki/let_expression x [[Date(2023-11-22T13:06:58)]]
----
[[WpEn:Let_expression]] = https://en.wikipedia.org/wiki/Let_expression
... Naver:"let expression" Ggl:"let expression"
} // let expression

[[정규식,regular_expression,regex]] - [[VG:정규식,regular_expression,regexp]]

[[논리식,logical_expression]] ? - 현재 [[논리식,logic_formula]] [[논리식,logical_formula]] 페이지는 있는데... TBD

[[식트리,expression_tree]] - [[트리,tree]]
{
MKLINK
[[abstract_syntax_tree]] (AST)
[[계산그래프,computational_graph]]

WpEn:Expression_tree redir to WpEn:Binary_expression_tree ([[Date(2023-07-20T12:00:35)]])
... Google:expression.tree
}

[[불_식,boolean_expression]]

[[free_expression]] =,free_expression . free_expression { 모든 변수가 [[free_variable]]인 expression. https://wiki.haskell.org/Free_expression .... WtEn:free_expression ? Sub: [[maximal_free_expression]] ... Ggl:"free expression" Bing:"free expression" }
 [[maximal_free_expression]] { https://wiki.haskell.org/Maximal_free_expression ... Ggl:"maximal free expression" Bing:"maximal free expression" }

[[subexpression]] =,subexpression . subexpression
{
부식? 부분식?

KmsE:subexpression ?
WtEn:subexpression ?

[[common_subexpression_elimination]] =,common_subexpression_elimination . common_subexpression_elimination
 WtEn:common_subexpression_elimination ?

}

[[proper_subexpression]] =,proper_subexpression . proper_subexpression
{
proper subexpression
진부식 ? 진부분식?

[[WtEn:proper_subexpression]]

... Ggl:"proper subexpression"
"proper subexpression"
}

[[reducible_expression]] = [[redex]]
=,reducible_expression | =,redex .
{
[[reduction]] 가능한 식?
https://wiki.haskell.org/Reducible_expression

WtEn:reducible_expression
WtEn:redex

... Google:reducible.expression
}

[[algebraic_expression]] =,algebraic_expression =,algebraic_expression . algebraic_expression
대수식 ?
대수적 식 ?
대수적 수식 ? ...
MKL
 algebraic_function 대수함수 (wk) 대수적 함수 Opp. "Nonalgebraic functions are called transcendental_function s."(mw)  https://mathworld.wolfram.com/AlgebraicFunction.html  https://en.wikipedia.org/wiki/Algebraic_function https://ko.wikipedia.org/wiki/대수함수 https://planetmath.org/AlgebraicFunction Up: [[함수,function]]
 algebraic_equation "algebraic equation or polynomial equation"(we) AKA: polynomial_equation =,polynomial_equation . https://mathworld.wolfram.com/AlgebraicEquation.html https://en.wikipedia.org/wiki/Algebraic_equation
 algebraic_operation 대수연산 ? 대수적 연산 https://en.wikipedia.org/wiki/Algebraic_operation Up: [[연산,operation]]
https://en.wikipedia.org/wiki/Algebraic_expression
 algebraic_number "The roots of an algebraic_equation in one variable are known as '''algebraic number'''s."[* https://mathworld.wolfram.com/AlgebraicEquation.html]
  https://mathworld.wolfram.com/AlgebraicNumber.html
 transcendental_function =,transcendental_function . https://mathworld.wolfram.com/TranscendentalFunction.html
https://mathworld.wolfram.com/AlgebraicExpression.html


analytical_expression
analytical expression
"analytical expression"
대수식 ?
KmsE:"analytical expression"
Ndict:"analytical expression"
Ggl:"analytical expression"

arithmetic_expression
arithmetic expression
산술식 ?
"arithmetic expression"
KmsE:"arithmetic expression"
Ndict:"arithmetic expression"
Ggl:"arithmetic expression"

ADDHERE

----
식의 [[표현,expression]] [[표기법,notation]]에는
prefix_notation
infix_notation
suffix_notation
[[괄호,parenthesis]] 가 쓰임

MKLINK
[[시퀀트,sequent]]
[[명제,proposition]]

(수식) = 0 으로 두어 등식,equation 을 만들면 [[방정식,equation]]??

같은 영단어 다른 표현: '''expression'''의 가장 일반적인 뜻은 [[표현,expression]].

한국어 단어 '식'의 다른 뜻
[[식,]], [[VG:식,]] 그리고 [[expression]]으로 검색해 적당히 링크 - atom, formula 이런것들
[[방정식,equation]]
[[공식,formula]]
등식
[[부등식,inequality]] vg =부등식,inequality =,inequality . 부등식 inequality
{
https://ko.wikipedia.org/wiki/벨_부등식
https://simple.wikipedia.org/wiki/Bell%27s_theorem
https://en.wikipedia.org/wiki/Bell%27s_theorem
https://namu.wiki/w/벨의%20부등식
Ndict:"벨 부등식"
Ggl:"벨 부등식"
}
[[다항식,polynomial]]
점화식 recurrence_equation ? - curr. 점화관계. (curr. [[VG:점화식,recurrence_relation]])
...

= 유리식 =
[[유리식,rational_expression]]
KmsK:유리식
[[https://terms.naver.com/entry.naver?docId=3338429&cid=47324&categoryId=47324 수학백과: 유리식]]
Ndict:유리식

Ggl:유리식

= 무리식 ''// 이상 wikify TODO'' =
[[무리식]]
[[무리식,irrational_expression]]

WtEn:irrational_expression

[[https://terms.naver.com/entry.naver?docId=3338461&cid=47324&categoryId=47324 수학백과: 무리식]]
 [[근호]] ([[근호,radical_sign]] or [[근호,radical_symbol]])안의 
  삭제무방
  이건 [[closed_form]]? 근데 무한한 근호같은건 not? chk
 Cmp: [[유리식]]

Ndict:무리식

= atomic expression =
원자식
원자적 식

[[atomic_expression]] =,atomic_expression =,atomic_expression . atomic_expression
{
atomic expression

WtEn:atomic_expression ?

ex. PL에선 이런 것들
https://narucode.org/0/원자적_표현식

REL: [[원자식,atom]](atomic_formula) 

"atomic expression"
Ggl:"atomic expression"

} // atomic_expression

= Compare: expression vs statement =
쉬운 뻔한거지만.. 그래도 tbw - 특히 pl에 따라 ([[제어구조,control_structure]] [[제어흐름,control_flow]] 인) if-else suite가 단순히 statement인 경우도 있는데, expression인 경우도 있어서 이런것들은 정리할 필요가 있다

[[statement]]의 번역 결정 후.

expression vs statement
https://mingyuchoo.hashnode.dev/expression-vs-statement


= 영단어 expression의 다른 뜻 =
[[표현,expression]]
최근에는 expression을 '표현식'으로 번역하기도 하는데... 이게 좋은건지 나쁜건지 ...?

----
[[WtEn:expression]] = https://en.wiktionary.org/wiki/expression

CS에서 식

[[WpKo:식_(프로그래밍)]]
= https://ko.wikipedia.org/wiki/식_%28프로그래밍%29

[[WpEn:Expression_(computer_science)]]
= https://en.wikipedia.org/wiki/Expression_%28computer_science%29

수식

[[WpKo:수식]]
= https://ko.wikipedia.org/wiki/수식

[[WpEn:Expression_(mathematics)]] = mathematical_expression = 수식
= https://en.wikipedia.org/wiki/Expression_(mathematics)
= https://en.wikipedia.org/wiki/Expression_%28mathematics%29