모노이드,monoid

결합법칙 만족
...

//eom
semigroup with identity


i.e.
"추상대수학에서 모노이드항등원,identity_element을 갖는, 결합법칙,associativity을 따르는 이항연산,binary_operation을 갖춘 대수구조,algebraic_structure이다. 군,group의 정의에서 역원,inverse_element의 존재를 생략하거나, 반군,semigroup(semigroup)의 정의에서 항등원,identity_element의 존재를 추가하여 얻는다."

1. Sub


1.1. trivial monoid

1.4.1. closed monoidal category

closed_monoidal_category
Ggl:closed monoidal category

1.5. submonoid

1.7. syntactic monoid

syntactic_monoid =,syntactic_monoid . syntactic_monoid
{
syntactic monoid



1.8. trace monoid

trace_monoid =,trace_monoid . trace_monoid

WtEn:trace_monoid x (2023-08-17)
https://en.wikipedia.org/wiki/Trace_monoid
trace는 문자열,string. =,trace . trace { Sub: trace_cache =,trace_cache =,trace_cache . trace_cache
{
(we)"In 컴퓨터구조,computer_architecture,
a trace cache or execution trace cache
is a specialized instruction_cache { instruction_cache WtEn:instruction_cache }
which stores the dynamic stream of 명령어,instructions 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 monoids."
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://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) { ktrace이게 생성한 것은 kdump로 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_(computer_programming) 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 }
....
}
........ADDHERE.........

2. Topics:


3. MKL

semigroup - 반군,semigroup(잠정적pagename)
항등원,identity_element // semigroup + 항등원 => 모노이드


6. tmp video en

Monoids | Group theory episode 1 - YouTube / All Angles
https://www.youtube.com/watch?v=dYN8Q4Ms5U4
{
easy. 22m.

군론,group_theory series에서 첫번째 ep인 듯

가장 간단한 예는 (set of natural numbers) with (addition).
$\displaystyle (N,+)$
여기서 $\displaystyle N=\{0,1,2,3,4,\ldots\}$
$\displaystyle N$ 은 closed under addition.
neutral/identity element 포함. 저것은 $\displaystyle +$ 에 대한 효과가 없음(no effect).
$\displaystyle +$ 은 binary operation.
associative. $\displaystyle (a+b)+c = a+(b+c)$

또 다른 예는 string(원소에 empty string 포함, 연산은 concatenation)
  • strings are closed under concatenation. ✔️
  • concatenation is associative. (ab)c=a(bc). ✔️
  • empty string is neutral/identity element. ✔️
따라서 monoid의 조건 만족.

원 색칠(파랑 노랑)으로 비유하는데 .... 왜 명령어,instruction들로 이루어진 subroutine의 실행,execution이 monoid에 비유되는지 알 수 있다. (semicolon ; is binary operation)
입출력,IO도 마찬가지.
for_loop 도.
암튼 PL의 스테이트먼트,statements' 대수적algebraic 추상화,abstraction에 쓰임.

인버스,inverse는 없다 ... 저게 포함되려면 군,group

}