Difference between r1.9 and the current
@@ -1,4 +1,7 @@
#noindex
//eom
semigroup with identity
결합법칙 만족
...
semigroup with identity
@@ -29,22 +32,24 @@
[[free_monoid]] =,free_monoid . free_monoid
{
https://encyclopediaofmath.org/wiki/Free_semi-group
''(Redirected from Free monoid)''
[[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:free_monoid
[[WtEn:free_monoid]]
= https://en.wiktionary.org/wiki/free_monoid
"(algebra) A monoid whose WtEn:underlying_set is the WtEn:Kleene_closure of some set of generator^^[[제너레이터,generator]]^^s, and whose operator^^[[연산자,operator]]^^ is concatenation^^[[concatenation]]^^."
[[WpEn:Free_monoid]]
= https://en.wikipedia.org/wiki/Free_monoid
https://encyclopediaofmath.org/wiki/Free_semi-group
''(Redirected from Free monoid)''
REL/MKL:
[[단어,word]][[알파벳,alphabet]]
[[문자열,string]]
}
== monoid object ==
[[모노이드대상,monoid_object]] - [[대상,object]]
== monoidal category ==
[[monoidal_category]] =,monoidal_category . monoidal_category
@@ -54,6 +59,8 @@
Sub: [[closed_monoidal_category]]
https://en.wiktionary.org/wiki/monoidal_category
Ndict:"monoidal category"
@@ -73,18 +80,39 @@
Ggl:submonoid
== 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
trace_cache
execution trace cache
== history monoid ==
history_monoid =,history_monoid . history_monoid
[[history_monoid]] =,history_monoid . history_monoid w
MKL
[[CCS,calculus_of_communicating_systems]]
WtEn:history_monoid x ([[Date(2023-08-16T15:59:02)]])
https://en.wikipedia.org/wiki/History_monoid
Ggl:"history monoid"
== syntactic monoid ==
[[syntactic_monoid]] =,syntactic_monoid . syntactic_monoid
{
'''syntactic monoid'''
https://en.wikipedia.org/wiki/Syntactic_monoid
WtEn:syntactic_monoid x 2024-03
} // syntactic monoid .... Naver:"syntactic monoid" Bing:"syntactic monoid" Ggl:"syntactic 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."
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,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 cachetrace_cache
execution trace cache
@@ -97,6 +125,7 @@
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 .
[[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 .
@@ -150,6 +179,40 @@
= tmp bmks en =
https://typeclasses.com/monoid
= Inter =
https://artofproblemsolving.com/wiki/index.php/Monoid
https://typeclasses.com/monoid
= 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).
$(N,+)$
여기서 $N=\{0,1,2,3,4,\ldots\}$
$N$ 은 closed under addition.
neutral/identity element 포함. 저것은 $+$ 에 대한 효과가 없음(no effect).
$+$ 은 binary operation.
associative. $(a+b)+c = a+(b+c)$
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,instruction]]들로 이루어진 subroutine의 [[실행,execution]]이 monoid에 비유되는지 알 수 있다. (semicolon ; is binary operation)
[[입출력,IO]]도 마찬가지.
for_loop 도.
암튼 PL의 [[스테이트먼트,statement]]s' 대수적algebraic [[추상화,abstraction]]에 쓰임.
[[인버스,inverse]]는 없다 ... 저게 포함되려면 [[군,group]]
}
...
YouTube:"monoid algebra"
https://artofproblemsolving.com/wiki/index.php/Monoid
결합법칙 만족
...
...
//eom
semigroup with identity
semigroup with identity
//wpko
항등원,identity_element을 갖는
결합법칙,associativity을 따르는
이항연산,binary_operation을 갖춘 대수구조,algebraic_structure.
항등원,identity_element을 갖는
결합법칙,associativity을 따르는
이항연산,binary_operation을 갖춘 대수구조,algebraic_structure.
i.e.
"추상대수학에서 모노이드는 항등원,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."
"추상대수학에서 모노이드는 항등원,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."
1.2. free monoid ¶
free_monoid
= https://en.wiktionary.org/wiki/free_monoid
= https://en.wikipedia.org/wiki/Free_monoid
= https://en.wiktionary.org/wiki/free_monoid
"(algebra) A monoid whose underlying_set is the Kleene_closure of some set of generator제너레이터,generators, and whose operator연산자,operator is concatenationconcatenation."
Free_monoid= https://en.wikipedia.org/wiki/Free_monoid
https://encyclopediaofmath.org/wiki/Free_semi-group
단어,word
알파벳,alphabet
문자열,string
(Redirected from Free monoid)
REL/MKL:단어,word
알파벳,alphabet
문자열,string
}
1.4. monoidal category ¶
monoidal_category =,monoidal_category . monoidal_category
monoidal_category
forkto 모노이드범주,monoidal_category
범주,category
monoidal_category
forkto 모노이드범주,monoidal_category
범주,category
1.5. submonoid ¶
submonoid
=,submonoid . submonoid
부분 모노이드
부분모노이드,submonoid
https://mathworld.wolfram.com/Submonoid.html
submonoid
submonoid
=,submonoid . submonoid
부분 모노이드
부분모노이드,submonoid
https://mathworld.wolfram.com/Submonoid.html
submonoid
submonoid
1.7. syntactic monoid ¶
syntactic_monoid x 2024-03
} // syntactic monoid .... syntactic monoid syntactic monoid syntactic monoid
} // syntactic monoid .... syntactic monoid syntactic monoid syntactic monoid
1.8. trace monoid ¶
trace_monoid =,trace_monoid . trace_monoid
trace_monoid x (2023-08-17)
https://en.wikipedia.org/wiki/Trace_monoid
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
}
https://en.wikipedia.org/wiki/Trace_monoid
trace는 문자열,string. =,trace . trace { Sub: trace_cache =,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 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."
a trace cache or execution trace cache
is a specialized instruction_cache { instruction_cache 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
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
= https://en.wikipedia.org/wiki/Tracing_(software)
= https://en.wikipedia.org/wiki/Tracing_(software)
cmp event_logging
Tracing_(software)= https://en.wikipedia.org/wiki/Tracing_(software)
= https://en.wikipedia.org/wiki/Tracing_(software)
https://en.wikipedia.org/wiki/Trace_theory
DTrace (FreeBSD and SmartOS) { https://ko.wikipedia.org/wiki/DTrace https://en.wikipedia.org/wiki/DTrace 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) {
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 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 LTTng }
SystemTap (Linux_kernel tracing tool) { SystemTap (stap) scripting_language and tool for dynamic instrumentation =,instrumentation . instrumentation { instrumentation https://ko.wikipedia.org/wiki/인스트루먼테이션 Instrumentation_(computer_programming) = https://en.wikipedia.org/wiki/Instrumentation_(computer_programming) = https://en.wikipedia.org/wiki/Instrumentation_(computer_programming) trace instrumentation } https://ko.wikipedia.org/wiki/SystemTap https://en.wikipedia.org/wiki/SystemTap SystemTap }
truss
ProbeVue (IBM AIX lightweight dynamic tracing environment) { https://en.wikipedia.org/wiki/ProbeVue ProbeVue }
....
}
........ADDHERE.........
DTrace (FreeBSD and SmartOS) { https://ko.wikipedia.org/wiki/DTrace https://en.wikipedia.org/wiki/DTrace 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 ... eBPF eBPF 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 ktrace }https://en.wikipedia.org/wiki/EBPF ... eBPF eBPF eBPF }
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 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 LTTng }
SystemTap (Linux_kernel tracing tool) { SystemTap (stap) scripting_language and tool for dynamic instrumentation =,instrumentation . instrumentation { instrumentation https://ko.wikipedia.org/wiki/인스트루먼테이션 Instrumentation_(computer_programming) = https://en.wikipedia.org/wiki/Instrumentation_(computer_programming) = https://en.wikipedia.org/wiki/Instrumentation_(computer_programming) trace instrumentation } https://ko.wikipedia.org/wiki/SystemTap https://en.wikipedia.org/wiki/SystemTap SystemTap }
truss
ProbeVue (IBM AIX lightweight dynamic tracing environment) { https://en.wikipedia.org/wiki/ProbeVue ProbeVue }
....
}
........ADDHERE.........
6. tmp video en ¶
Monoids | Group theory episode 1 - YouTube / All Angles
https://www.youtube.com/watch?v=dYN8Q4Ms5U4
{
easy. 22m.
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).
$\displaystyle N$ 은 closed under 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. ✔️
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.
입출력,IO도 마찬가지.
for_loop 도.
암튼 PL의 스테이트먼트,statements' 대수적algebraic 추상화,abstraction에 쓰임.
}
7. Inter ¶
https://everything2.com/title/monoid
{
번역at2023-09-26
Monoid는 거의 군,group이다. 유일하게 군의 조건을 만족하지 못하는 것이 그 안의 모든 원소,element가 인버스,inverse(역,inverse 역원,inverse_element?)을 가질 필요가 없다는 점이다.
모노이드는 항등원,identity_element을 가진다(이 특징을 semigroup과 대조해 보라.) - TBW
Contrast: semigroup
}
{
번역at2023-09-26
Monoid는 거의 군,group이다. 유일하게 군의 조건을 만족하지 못하는 것이 그 안의 모든 원소,element가 인버스,inverse(역,inverse 역원,inverse_element?)을 가질 필요가 없다는 점이다.
모노이드는 항등원,identity_element을 가진다(이 특징을 semigroup과 대조해 보라.) - TBW
Contrast: semigroup
}
Monoid_(category_theory)
= https://en.wikipedia.org/wiki/Monoid_(category_theory)
= https://en.wikipedia.org/wiki/Monoid_(category_theory)
= https://en.wikipedia.org/wiki/Monoid_(category_theory)
= https://en.wikipedia.org/wiki/Monoid_(category_theory)