#noindex
//eom
semigroup with identity

//wpko
[[항등원,identity_element]]을 갖는
[[결합법칙,associativity]]을 따르는
[[이항연산,binary_operation]]을 갖춘 [[대수구조,algebraic_structure]].

i.e.
"추상대수학에서 '''모노이드'''는 [[항등원,identity_element]]을 갖는, [[결합법칙,associativity]]을 따르는 [[이항연산,binary_operation]]을 갖춘 [[대수구조,algebraic_structure]]이다. [[군,group]]의 정의에서 [[역원,inverse_element]]의 존재를 생략하거나, [[반군,semigroup]]([[semigroup]])의 정의에서 [[항등원,identity_element]]의 존재를 추가하여 얻는다."
<<tableofcontents>>
= Sub =

== trivial monoid ==
trivial_monoid
WpEn:Trivial_monoid

via
 [[trivial_group]] - [[군,group]]

cmp
 [[trivial_group]]
 [[trivial_ring]]

Up: [[trivial]]

== free monoid ==
[[free_monoid]] =,free_monoid . free_monoid
{

WtEn:free_monoid

https://encyclopediaofmath.org/wiki/Free_semi-group
 ''(Redirected from Free monoid)''
[[단어,word]]
[[알파벳,alphabet]]

}
== monoid object ==
[[모노이드대상,monoid_object]] - [[대상,object]]
=,monoid_object . monoid_object

WtEn:monoid_object x ([[Date(2023-08-16T15:59:02)]])

Ndict:"monoid object"
Ggl:"monoid object"

== monoidal category ==
[[monoidal_category]] =,monoidal_category . monoidal_category
WtEn:monoidal_category
forkto [[모노이드범주,monoidal_category]]
[[범주,category]]

Sub: [[closed_monoidal_category]]

https://en.wikipedia.org/wiki/Monoidal_category

Ndict:"monoidal category"
Ggl:"monoidal category"

=== closed monoidal category ===
closed_monoidal_category
Ggl:"closed monoidal category"

== submonoid ==
submonoid
=,submonoid . submonoid 
부분 모노이드
[[부분모노이드,submonoid]]
https://mathworld.wolfram.com/Submonoid.html
Ndict:submonoid 
Ggl:submonoid 

== history monoid ==
history_monoid =,history_monoid . history_monoid

WtEn:history_monoid x ([[Date(2023-08-16T15:59:02)]])
https://en.wikipedia.org/wiki/History_monoid
Ggl:"history monoid"

== trace monoid ==
trace_monoid =,trace_monoid . trace_monoid

WtEn:trace_monoid x ([[Date(2023-08-16T15:59:02)]])
https://en.wikipedia.org/wiki/Trace_monoid
 trace는 [[문자열,string]]. =,trace . trace { Sub: trace_cache =,trace_cache . trace_cache { (we)"In [[computer_architecture]], a '''trace cache''' or '''execution trace cache''' is a specialized instruction_cache which stores the dynamic stream of instruction s known as '''trace'''. ..... A '''trace processor''' is an architecture designed around the trace cache and processes the instructions at trace level granularity. The formal mathematical theory of traces is described by '''trace monoid'''s."
trace cache
trace_cache
execution trace cache
execution_trace_cache
instruction cache
instruction_cache
trace processor
trace_processor
trace monoid
trace_monoid
[[명령어,instruction]] [[실행,execution]] [[트레이스,trace]]? [[캐시,cache]] [[프로세서,processor]] [[모노이드,monoid]]
https://en.wikipedia.org/wiki/Trace_cache

기타 trace / tracing 에 대해 더: =,trace =,tracing .

https://ko.wikipedia.org/wiki/트레이싱
 cmp event_logging

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

https://en.wikipedia.org/wiki/Branch_trace

https://en.wikipedia.org/wiki/Trace_theory
 concurrent_computation { https://en.wikipedia.org/wiki/Concurrent_computation }, process_calculus 

DTrace (FreeBSD and SmartOS) { https://ko.wikipedia.org/wiki/DTrace https://en.wikipedia.org/wiki/DTrace Bing:dtrace }
ftrace (Linux_kernel) https://en.wikipedia.org/wiki/Ftrace
WPP(?) (Windows) https://en.wikipedia.org/wiki/Windows_software_trace_preprocessor
''그리고 추가로 비슷한것들, via https://en.wikipedia.org/wiki/DTrace#See_also :''
eBPF (Linux_kernel) {
 BPF : Berkeley_Packet_Filter { '''Berkeley Packet Filter (BPF)''' https://en.wikipedia.org/wiki/Berkeley_Packet_Filter }
 https://en.wikipedia.org/wiki/EBPF ... Naver:"eBPF" Bing:"eBPF" Ggl:"eBPF" }
ktrace (BSD and macOS, kernel-program interaction tracer) { '''ktrace'''이게 생성한 것은 [[kdump]]로 읽는다. https://ko.wikipedia.org/wiki/Ktrace  https://en.wikipedia.org/wiki/Ktrace Naver:ktrace }
ltrace (Linux, userland application이 [[shared_library]] =,shared_library . shared_library { shared_library = shared_object .... https://en.wikipedia.org/wiki/Shared_library }호출하는 것을 보여주는 debugging utility) { (동적로딩 dynamic_loading 동적링킹 dynamic_linking linked to: https://ko.wikipedia.org/wiki/동적_적재 https://en.wikipedia.org/wiki/Dynamic_loading https://en.wikipedia.org/wiki/Dynamic_linker (Redirected from WpEn:Dynamic_linking) )시스템을 hooking ... shim 을 삽입 ... static_linking(rel static_library = statically-linked_library  .. linked to: https://ko.wikipedia.org/wiki/정적_라이브러리 https://en.wikipedia.org/wiki/Static_library ) 된 호출들은 trace할 수 없음. ...  https://ko.wikipedia.org/wiki/Ltrace https://en.wikipedia.org/wiki/Ltrace }
strace (Linux, system_call 및 signal 을 모니터링하는 debugging utility) https://en.wikipedia.org/wiki/Strace
LTT Linux Trace Toolkit (LTT) { https://en.wikipedia.org/wiki/Linux_Trace_Toolkit }
''and''
LTTng Linux Trace Toolkit Next Generation (LTTng)  {https://en.wikipedia.org/wiki/LTTng Ggl:LTTng }
SystemTap (Linux_kernel tracing tool) { '''SystemTap (stap)''' scripting_language and tool for dynamic instrumentation =,instrumentation . instrumentation  { instrumentation https://ko.wikipedia.org/wiki/인스트루먼테이션  [[WpEn:Instrumentation_(computer_programming)]] = https://en.wikipedia.org/wiki/Instrumentation_(computer_programming) =  https://en.wikipedia.org/wiki/Instrumentation_%28computer_programming%29  Ggl:trace+instrumentation } https://ko.wikipedia.org/wiki/SystemTap https://en.wikipedia.org/wiki/SystemTap  Naver:SystemTap  }
truss 
ProbeVue (IBM AIX lightweight dynamic tracing environment) { https://en.wikipedia.org/wiki/ProbeVue Naver:ProbeVue }
....
}
 [[process_calculus]] 등 [[concurrent_computation]]에 쓰임.
 [[history_monoid]]와 isomorphic([[동형사상,isomorphism]]).


........ADDHERE.........
= Topics: =

= MKL =
[[semigroup]] - [[반군,semigroup]](잠정적pagename)
[[항등원,identity_element]] // semigroup + 항등원 => '''모노이드'''

Cmp [[모나드,monad]]

= tmp bmks ko =
https://wikidocs.net/1747
https://en.wikibooks.org/wiki/Haskell/Monoids 의 번역

= tmp bmks en =
https://typeclasses.com/monoid
= Inter =
https://artofproblemsolving.com/wiki/index.php/Monoid

https://mathworld.wolfram.com/Monoid.html

https://everything2.com/title/monoid

https://groupprops.subwiki.org/wiki/Monoid

https://encyclopediaofmath.org/wiki/Monoid

https://namu.wiki/w/모노이드

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

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

https://ncatlab.org/nlab/show/monoid

... Google:monoid Naver:monoid
... Google:모노이드 Naver:모노이드

Up:
[[추상대수,abstract_algebra]]