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16,243 |
Wikijunior:ãšã¹ãã©ã³ãããã/ããã
|
ããã - DolÄaĵo - (ãã«ãã£ãŒãžã§)
ã»ã»ã» Kuko - (ã¯ãŒã³)
ã»ã»ã» Kuketo - (ã¯ã±ãŒã)
ã»ã»ã» Äokolado - (ãã§ã³ã©ãŒã)
ã»ã»ã» Bombon - (ãã ããŒã)
ã»ã»ã» Rizkrakeno - (ãªãºã¯ã©ã±ãŒã)
|
[
{
"paragraph_id": 0,
"tag": "p",
"text": "ããã - DolÄaĵo - (ãã«ãã£ãŒãžã§)",
"title": ""
},
{
"paragraph_id": 1,
"tag": "p",
"text": "ã»ã»ã» Kuko - (ã¯ãŒã³)",
"title": "ã±ãŒã"
},
{
"paragraph_id": 2,
"tag": "p",
"text": "",
"title": "ã±ãŒã"
},
{
"paragraph_id": 3,
"tag": "p",
"text": "ã»ã»ã» Kuketo - (ã¯ã±ãŒã)",
"title": "ã¯ãããŒ"
},
{
"paragraph_id": 4,
"tag": "p",
"text": "",
"title": "ã¯ãããŒ"
},
{
"paragraph_id": 5,
"tag": "p",
"text": "ã»ã»ã» Äokolado - (ãã§ã³ã©ãŒã)",
"title": "ãã§ã³ã¬ãŒã"
},
{
"paragraph_id": 6,
"tag": "p",
"text": "",
"title": "ãã§ã³ã¬ãŒã"
},
{
"paragraph_id": 7,
"tag": "p",
"text": "ã»ã»ã» Bombon - (ãã ããŒã)",
"title": "ãã"
},
{
"paragraph_id": 8,
"tag": "p",
"text": "",
"title": "ãã"
},
{
"paragraph_id": 9,
"tag": "p",
"text": "ã»ã»ã» Rizkrakeno - (ãªãºã¯ã©ã±ãŒã)",
"title": "ããã¹ã"
},
{
"paragraph_id": 10,
"tag": "p",
"text": "",
"title": "ããã¹ã"
}
] |
ããã - DolÄaĵo - (ãã«ãã£ãŒãžã§)
|
<big><big><big>ããã - [[wikt:dolÄaĵo|DolÄaĵo]]<!--BRO3--> - (ãã«ãã£ãŒãžã§)</big></big></big>
== ã±ãŒã ==
[[File:ã·ã§ãŒãã±ãŒãP3192821.JPG|200px]]
<big><big><big>ã»ã»ã» [[wikt:kuko|Kuko]]<!--BRO5--> - (ã¯ãŒã³)</big></big></big>
----<br>
== ã¯ãã㌠==
[[File:Choco chip cookie.jpg|200px]]
<big><big><big>ã»ã»ã» [[wikt:kuketo|Kuketo]]<!--BRO5--> - (ã¯ã±ãŒã)</big></big></big>
----<br>
== ãã§ã³ã¬ãŒã ==
[[File:Chocolate.jpg|200px]]
<big><big><big>ã»ã»ã» [[wikt:Äokolado|Äokolado]]<!--BRO7--> - (ãã§ã³ã©ãŒã)</big></big></big>
----<br>
== ãã ==
[[File:Candy.jpg|200px]]
<big><big><big>ã»ã»ã» [[wikt:bombono|Bombon]]<!--BRO8--> - (ãã ããŒã)</big></big></big>
----<br>
== ããã¹ã ==
[[File:Taishakuten Sando -03.jpg|200px]]
<big><big><big>ã»ã»ã» [[wikt:rizkrakeno|Rizkrakeno]]<!--éå
¬åŒ--> - (ãªãºã¯ã©ã±ãŒã)</big></big></big>
----<br>
[[Category:ãšã¹ãã©ã³ã (ãŠã£ããžã¥ãã¢)|åèª ããã]]
| null |
2015-08-30T01:53:50Z
|
[] |
https://ja.wikibooks.org/wiki/Wikijunior:%E3%82%A8%E3%82%B9%E3%83%9A%E3%83%A9%E3%83%B3%E3%83%88%E3%81%9F%E3%82%93%E3%81%94/%E3%81%8A%E3%81%8B%E3%81%97
|
16,244 |
ãããã/ç·Žç¿1
|
ããããã®çºé³ã·ã¹ãã ã¯æ¥æ¬èªãšã»ãŒåããªã®ã§ãã ããã9ã€ã®åé³ãk, s, t, n, p, m, j, l, wããš5ã€ã®æ¯é³ãa, i, u, e, oããããããŸããã
ã¢è¡ãå«ããŠãæ¥æ¬èªã®äºåé³ã«å¯Ÿå¿ããŸãã åé³ãjãã¯ããŒãåã®ãyãã«ããããŸãã ä»»æã«æ¿ç¹ãä»ããŠãæž
é³ãæ¿é³ã«çºé³ããŠãããŸããŸããã
ãããã®é³ç¯ããæ§æãããåèªã¯å
šãŠä»¥äžã®ç¹åŸŽãæã¡ãŸãã
ããããã®åèªã¯æé ãæ®µèœã®é ã§ãã£ãŠãåžžã«å°æåã§æžã衚ãããŸãã 倧æåã¯åœåã人åãªã©ã倿¥èªã§ããåºæåè©ã®é æåã«ãã䜿çšãããŸããã
倿¥èªã衚èšã»çºé³ãããšãã¯ããããã®çºé³ã«åãããŸãã ãŸãåé³ãå€ããšãã¯ãé³ç¯æ°ãç¶æããããã«ããŠå€éããåé³ãåããŸãã
æ¥æ¬èªã§ã¯å€æ¥èªãåãå
¥ãããšãã¯åé³ã«å¿ å®ããŸãã ãŸãåé³ãå
šéšåãå
¥ããŠãããã«æ¬æ¥ååšããªãã¯ãã®æ¯é³ã远å ããã ãEnglishã â ãã€ã³ã°ãªãã·ã¥ = Ingurisshuã
çŽç©ã¯åè§ã®ãã®ã䜿ãããã:ãã¯åŸã«ç¶ãæç« ãåã®æç« ã®ç¯ãšããããšã衚ããŸãã
|
[
{
"paragraph_id": 0,
"tag": "p",
"text": "ããããã®çºé³ã·ã¹ãã ã¯æ¥æ¬èªãšã»ãŒåããªã®ã§ãã ããã9ã€ã®åé³ãk, s, t, n, p, m, j, l, wããš5ã€ã®æ¯é³ãa, i, u, e, oããããããŸããã",
"title": "çºé³"
},
{
"paragraph_id": 1,
"tag": "p",
"text": "ã¢è¡ãå«ããŠãæ¥æ¬èªã®äºåé³ã«å¯Ÿå¿ããŸãã åé³ãjãã¯ããŒãåã®ãyãã«ããããŸãã ä»»æã«æ¿ç¹ãä»ããŠãæž
é³ãæ¿é³ã«çºé³ããŠãããŸããŸããã",
"title": "çºé³"
},
{
"paragraph_id": 2,
"tag": "p",
"text": "ãããã®é³ç¯ããæ§æãããåèªã¯å
šãŠä»¥äžã®ç¹åŸŽãæã¡ãŸãã",
"title": "çºé³"
},
{
"paragraph_id": 3,
"tag": "p",
"text": "ããããã®åèªã¯æé ãæ®µèœã®é ã§ãã£ãŠãåžžã«å°æåã§æžã衚ãããŸãã 倧æåã¯åœåã人åãªã©ã倿¥èªã§ããåºæåè©ã®é æåã«ãã䜿çšãããŸããã",
"title": "æžæ³"
},
{
"paragraph_id": 4,
"tag": "p",
"text": "倿¥èªã衚èšã»çºé³ãããšãã¯ããããã®çºé³ã«åãããŸãã ãŸãåé³ãå€ããšãã¯ãé³ç¯æ°ãç¶æããããã«ããŠå€éããåé³ãåããŸãã",
"title": "æžæ³"
},
{
"paragraph_id": 5,
"tag": "p",
"text": "",
"title": "æžæ³"
},
{
"paragraph_id": 6,
"tag": "p",
"text": "",
"title": "æžæ³"
},
{
"paragraph_id": 7,
"tag": "p",
"text": "æ¥æ¬èªã§ã¯å€æ¥èªãåãå
¥ãããšãã¯åé³ã«å¿ å®ããŸãã ãŸãåé³ãå
šéšåãå
¥ããŠãããã«æ¬æ¥ååšããªãã¯ãã®æ¯é³ã远å ããã ãEnglishã â ãã€ã³ã°ãªãã·ã¥ = Ingurisshuã",
"title": "æžæ³"
},
{
"paragraph_id": 8,
"tag": "p",
"text": "",
"title": "æžæ³"
},
{
"paragraph_id": 9,
"tag": "p",
"text": "çŽç©ã¯åè§ã®ãã®ã䜿ãããã:ãã¯åŸã«ç¶ãæç« ãåã®æç« ã®ç¯ãšããããšã衚ããŸãã",
"title": "æžæ³"
}
] | null |
== çºé³ ==
[[File:Pronunciation Toki Pona.png|360px|thumb|䜿çšããã14åã®ã©ãã³æå]]
ããããã®çºé³ã·ã¹ãã ã¯æ¥æ¬èªãšã»ãŒ'''åã'''ãªã®ã§ãã<br>
ããã9ã€ã®åé³ãk, s, t, n, p, m, j, l, wããš5ã€ã®æ¯é³ãa, i, u, e, oããããããŸããã
ã¢è¡ãå«ããŠãæ¥æ¬èªã®'''äºåé³'''ã«å¯Ÿå¿ããŸãã<br>
åé³ãjãã¯ããŒãåã®ãyãã«ããããŸãã<br>
ä»»æã«æ¿ç¹ãä»ããŠãæž
é³ãæ¿é³ã«çºé³ããŠãããŸããŸããã
{| class="wikitable" style="text-align: center"
|-
! width="35px"| !! width="35px"| - !! width="35px"| k !! width="35px"| s !! width="35px"| t !! width="35px"| n !! width="35px"| p !! width="35px"| m !! width="35px"| j !! width="35px"| l !! width="35px"| w
|-
! a
| 㢠|| ã« || ãµ || ã¿ || ã || ã || ã || 〠|| ã© || ã¯
|-
! i
| 〠|| ã || ã· || style="color: #bbb;"| (ã·) || ã || ã || ã || style="color: #bbb;"| (ã€) || 㪠|| ãŠã£
|-
! u
| ㊠|| 㯠|| ã¹ || ã㥠|| ã || ã || ã || ㊠|| ã« || style="color: #bbb;"| (ãŠ)
|-
! e
| ãš || ã± || ã» || ã || ã || ã || ã¡ || ã€ã§ || 㬠|| ãŠã§
|-
! o
| 㪠|| ã³ || 㜠|| ã || ã || ã || 㢠|| ãš || ã || style="color: #bbb;"| (ãª)
|}
{| class="wikitable" style="text-align: center"
|-
! width="35px"| n
| width="35px"| ã³
|}
* ãji, ti, wo, wuãã®é³ç¯ã¯ãããããi, si, o, uãã䜿çšãããŸãã<br>
:ïŒã·ãšãã®æ¿é³ã¯å€å¥ãã«ããããïŒ<br>
<br>
ãããã®é³ç¯ããæ§æãããåèªã¯å
šãŠä»¥äžã®ç¹åŸŽãæã¡ãŸãã
* ã¢ã¯ã»ã³ãã¯èªé
* ã¢è¡ã¯'''èªé '''ã®ã¿çŸãã
* ã'''ã³'''ãããå§ãŸããªã
* ãè¡ãšãè¡ã®çŽåã«ã¯ã'''ã³'''ãã¯ååšã§ããªã
== æžæ³ ==
=== æå ===
ããããã®åèªã¯æé ãæ®µèœã®é ã§ãã£ãŠã'''åžžã«å°æå'''ã§æžã衚ãããŸãã<br>
'''倧æå'''ã¯åœåã人åãªã©ã倿¥èªã§ãã'''åºæåè©'''ã®é æåã«ãã䜿çšãããŸããã<br>
<br>
=== 倿¥èª ===
倿¥èªã衚èšã»çºé³ãããšãã¯ããããã®çºé³ã«åãããŸãã<br>
ãŸãåé³ãå€ããšãã¯ãé³ç¯æ°ãç¶æããããã«ããŠå€éããåé³ãåããŸãã<br>
<br>
* ãã«ã»ãã â ãNijonãããšã³
: ããããã«ã¯ãè¡ãååšããªããããã»ããæ¬æ¥ãªããoããšãããšããã ãã<br>
: ãããšãNionããšãªã£ãŠã¢è¡ãèªäžã«çŸãããããæŽã«ãjããä»ãå ããŠããŸãã<br>
<br>
* ãEnglishã â ãInliãã€ã³ãª
: ããããã§ã¯ãæ¯é³æ°ãéèŠããŸããä»å±ã§ããªãåé³ã¯ãã¹ãŠçç¥ããŠããŸãã<br>
<br>
<div style="border: 1px solid grey; margin-left: 30px; padding: 0 10px; display: inline-block;">
æ¥æ¬èªã§ã¯å€æ¥èªãåãå
¥ãããšãã¯åé³ã«å¿ å®ããŸãã<br>
ãŸãåé³ãå
šéšåãå
¥ããŠãããã«æ¬æ¥ååšããªãã¯ãã®æ¯é³ã远å ããã<br>
ãEnglishã â ãã€ã³'''ã°'''ãª'''ãã·ã¥''' = Ing'''u'''rissh'''u'''ã
</div>
<br>
=== çŽç© ===
çŽç©ã¯'''åè§'''ã®ãã®ã䜿ãããã:ãã¯åŸã«ç¶ãæç« ãåã®æç« ã®ç¯ãšããããšã衚ããŸãã<br>
* äŸ) [[wikt:mi|mi]] [[wikt:pilin|pilin]] [[wikt:e|e]] [[wikt:ni|ni]]: [[wikt:toki|toki]] [[wikt:pona|pona]] [[wikt:li|li]] [[wikt:pona|pona]].
*: ç§ã¯æããããïŒããããã¯è¯ãã â ç§ã¯ãããããè¯ããšæãã
[[eo:Tokipono/Leciono_1]]
[[Category:ãããã|ç·Žç¿1]]
|
2011-07-16T00:30:01Z
|
2023-09-28T05:38:56Z
|
[] |
https://ja.wikibooks.org/wiki/%E3%83%88%E3%82%AD%E3%83%9D%E3%83%8A/%E7%B7%B4%E7%BF%921
|
16,245 |
ç Žç£æ³ç¬¬111æ¡
|
æ³åŠ>æ°äºæ³>ç Žç£æ³>ã³ã³ã¡ã³ã¿ãŒã«ç Žç£æ³(å)(次)
(ç Žç£åµæš©ã®å±åº)
|
[
{
"paragraph_id": 0,
"tag": "p",
"text": "æ³åŠ>æ°äºæ³>ç Žç£æ³>ã³ã³ã¡ã³ã¿ãŒã«ç Žç£æ³(å)(次)",
"title": ""
},
{
"paragraph_id": 1,
"tag": "p",
"text": "(ç Žç£åµæš©ã®å±åº)",
"title": "æ¡æ"
},
{
"paragraph_id": 2,
"tag": "p",
"text": "",
"title": "æ¡æ"
},
{
"paragraph_id": 3,
"tag": "p",
"text": "",
"title": "å€äŸ"
}
] |
æ³åŠïŒæ°äºæ³ïŒç Žç£æ³ïŒã³ã³ã¡ã³ã¿ãŒã«ç Žç£æ³ïŒåïŒïŒæ¬¡ïŒ
|
[[æ³åŠ]]ïŒ[[æ°äºæ³]]ïŒ[[ç Žç£æ³]]ïŒ[[ã³ã³ã¡ã³ã¿ãŒã«ç Žç£æ³]]ïŒ[[ç Žç£æ³ç¬¬110æ¡|å]]ïŒïŒ[[ç Žç£æ³ç¬¬112æ¡|次]]ïŒ
==æ¡æ==
ïŒç Žç£åµæš©ã®å±åºïŒ
;第111æ¡ ã
#ç Žç£æç¶ã«åå ããããšããç Žç£åµæš©è
ã¯ã[[ç Žç£æ³ç¬¬31æ¡|第31æ¡]]第1é
第äžå·åã¯ç¬¬3é
ã®èŠå®ã«ããå®ããããç Žç£åµæš©ã®å±åºããã¹ãæéïŒä»¥äžã嵿š©å±åºæéããšãããïŒå
ã«ãæ¬¡ã«æ²ããäºé
ãè£å€æã«å±ãåºãªããã°ãªããªãã
#:äž ãåç Žç£åµæš©ã®é¡åã³åå
#:äº ãåªå
çç Žç£åµæš©ã§ãããšãã¯ããã®æš
#:äž ãå£åŸçç Žç£åµæš©åã¯çŽå®å£åŸç Žç£åµæš©ã§ãããšãã¯ããã®æš
#:å ãèªå·±ã«å¯Ÿããé
åœé¡ã®åèšé¡ãæé«è£å€æèŠåã§å®ããé¡ã«æºããªãå Žåã«ãããŠãé
åœéãåé ããææããããšãã¯ããã®æš
#:äº ãååå·ã«æ²ãããã®ã®ã»ããæé«è£å€æèŠåã§å®ããäºé
#å¥é€æš©è
ã¯ãåé
åå·ã«æ²ããäºé
ã®ã»ããæ¬¡ã«æ²ããäºé
ãå±ãåºãªããã°ãªããªãã
#:äž ãå¥é€æš©ã®ç®çã§ãã財ç£
#:äº ãå¥é€æš©ã®è¡äœ¿ã«ãã£ãŠåŒæžãåããããšãã§ããªããšèŠèŸŒãŸãã嵿š©ã®é¡
#åé
ã®èŠå®ã¯ã[[ç Žç£æ³ç¬¬108æ¡|第108æ¡]]第2é
ã«èŠå®ããç¹å¥ã®å
åç¹æš©ã質暩è¥ããã¯æµåœæš©åã¯ç Žç£åµæš©ãæããè
ïŒä»¥äžãæºå¥é€æš©è
ããšãããïŒã«ã€ããŠæºçšããã
==解説==
*第31æ¡(ç Žç£æç¶éå§ã®æ±ºå®ãšåæã«å®ããã¹ãäºé
ç)
*第108æ¡(å¥é€æš©è
çã®æç¶åå )
==åç
§æ¡æ==
==å€äŸ==
*[http://www.courts.go.jp/search/jhsp0030?hanreiid=54259&hanreiKbn=02 ç Žç£åµæš©ç¢ºå®]ïŒæé«è£å€äŸ æå57幎01æ29æ¥ïŒ[[âæ°æ³ç¬¬152æ¡]]ïŒ/ç Žç£æ³240æ¡1é
*[]ïŒæé«è£å€äŸ ïŒ
{{stub}}
[[category:ç Žç£æ³|111]]
| null |
2011-07-16T05:08:55Z
|
[
"ãã³ãã¬ãŒã:Stub"
] |
https://ja.wikibooks.org/wiki/%E7%A0%B4%E7%94%A3%E6%B3%95%E7%AC%AC111%E6%9D%A1
|
16,246 |
Haskell/åè«
|
ãã®é
ç®ã§ã¯ Haskell ã«é¢é£ããå
容ã«éã£ãŠåè«ã®æŠèгãäžããããšã詊ã¿ãããã®ããã«ãæ°åŠçãªå®çŸ©ã«äœµã㊠Haskell ã³ãŒãã瀺ãã絶察çãªå³å¯ãã¯æ±ããªãããã®ããããåè«ã®æŠå¿µãšã¯ã©ããªãã®ããã©ã®ããã« Haskell ã«é¢é£ãããã®çŽæçãªçè§£ãèªè
ã«äžããããšã远æ±ããã
æ¬è³ªçã«ãåãšã¯åçŽãªéãŸãã§ãããããã¯æ¬¡ã®3ã€ã®èŠçŽ ãããªãã
æ§ã
ãªãã®ãåãã€ãããäŸãã°ãSet ã¯å
šãŠã®éåã察象ãšããå°ãšããŠæšæºçãªé¢æ°ãåæãšããŠéåžžã®é¢æ°åæãæã€åã§ããã(åã®ååã¯ãã°ãã°å€ªåã§è¡šãããã)Grpã¯å
šãŠã®çŸ€ã察象ãšããå°ãšããŠçŸ€ã®æŒç®ãä¿åãã颿°(矀æºåå)ãæã€åã§ãããã€ãŸããä»»æã®2ã€ã®çŸ€ G, H (ããããæŒç® â {\displaystyle *} , â
{\displaystyle \cdot } ããã€)ã«ã€ããŠã f ( u â v ) = f ( u ) â
f ( v ) {\displaystyle f(u*v)=f(u)\cdot f(v)} ãªãã°ããã€ãã®ãšãã«éãã f : G â H {\displaystyle f:G\to H} 㯠Grp å
ã®å°ã§ããã
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èŠã¯ãªããäŸãã°ããããªãåé åº (P, †{\displaystyle \leq } )ãåãå®çŸ©ãããããã§å¯Ÿè±¡ã¯Pã®èŠçŽ ã§ãããä»»æã®2ã€ã®å¯Ÿè±¡A, Bã«ã€ã㊠A †B {\displaystyle A\leq B} ã§ãããšããã€ãã®ãšãã«éãAãšBã®éã«å°ãååšããããŸããè€æ°ã®ç°ãªãå°ãåããœãŒã¹ãªããžã§ã¯ããšã¿ãŒã²ãããªããžã§ã¯ããæã€ããšãã§ãããSetã®äŸã§ããã°ã sin {\displaystyle \sin } ãš cos {\displaystyle \cos } ã¯ãããããœãŒã¹ãªããžã§ã¯ã R {\displaystyle \mathbb {R} } ãš ã¿ãŒã²ãããªããžã§ã¯ã [ â 1 , 1 ] {\displaystyle [-1,1]} ããã€ãããã¡ãããããã¯åãå°ã§ã¯ãªã!
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[
{
"paragraph_id": 0,
"tag": "p",
"text": "",
"title": ""
},
{
"paragraph_id": 1,
"tag": "p",
"text": "ãã®é
ç®ã§ã¯ Haskell ã«é¢é£ããå
容ã«éã£ãŠåè«ã®æŠèгãäžããããšã詊ã¿ãããã®ããã«ãæ°åŠçãªå®çŸ©ã«äœµã㊠Haskell ã³ãŒãã瀺ãã絶察çãªå³å¯ãã¯æ±ããªãããã®ããããåè«ã®æŠå¿µãšã¯ã©ããªãã®ããã©ã®ããã« Haskell ã«é¢é£ãããã®çŽæçãªçè§£ãèªè
ã«äžããããšã远æ±ããã",
"title": ""
},
{
"paragraph_id": 2,
"tag": "p",
"text": "æ¬è³ªçã«ãåãšã¯åçŽãªéãŸãã§ãããããã¯æ¬¡ã®3ã€ã®èŠçŽ ãããªãã",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 3,
"tag": "p",
"text": "æ§ã
ãªãã®ãåãã€ãããäŸãã°ãSet ã¯å
šãŠã®éåã察象ãšããå°ãšããŠæšæºçãªé¢æ°ãåæãšããŠéåžžã®é¢æ°åæãæã€åã§ããã(åã®ååã¯ãã°ãã°å€ªåã§è¡šãããã)Grpã¯å
šãŠã®çŸ€ã察象ãšããå°ãšããŠçŸ€ã®æŒç®ãä¿åãã颿°(矀æºåå)ãæã€åã§ãããã€ãŸããä»»æã®2ã€ã®çŸ€ G, H (ããããæŒç® â {\\displaystyle *} , â
{\\displaystyle \\cdot } ããã€)ã«ã€ããŠã f ( u â v ) = f ( u ) â
f ( v ) {\\displaystyle f(u*v)=f(u)\\cdot f(v)} ãªãã°ããã€ãã®ãšãã«éãã f : G â H {\\displaystyle f:G\\to H} 㯠Grp å
ã®å°ã§ããã",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 4,
"tag": "p",
"text": "å°ã¯ãã€ã颿°ã®ããã«ãæããããããã§ããå¿
èŠã¯ãªããäŸãã°ããããªãåé åº (P, †{\\displaystyle \\leq } )ãåãå®çŸ©ãããããã§å¯Ÿè±¡ã¯Pã®èŠçŽ ã§ãããä»»æã®2ã€ã®å¯Ÿè±¡A, Bã«ã€ã㊠A †B {\\displaystyle A\\leq B} ã§ãããšããã€ãã®ãšãã«éãAãšBã®éã«å°ãååšããããŸããè€æ°ã®ç°ãªãå°ãåããœãŒã¹ãªããžã§ã¯ããšã¿ãŒã²ãããªããžã§ã¯ããæã€ããšãã§ãããSetã®äŸã§ããã°ã sin {\\displaystyle \\sin } ãš cos {\\displaystyle \\cos } ã¯ãããããœãŒã¹ãªããžã§ã¯ã R {\\displaystyle \\mathbb {R} } ãš ã¿ãŒã²ãããªããžã§ã¯ã [ â 1 , 1 ] {\\displaystyle [-1,1]} ããã€ãããã¡ãããããã¯åãå°ã§ã¯ãªã!",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 5,
"tag": "p",
"text": "",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 6,
"tag": "p",
"text": "åãåŸããªããã°ãªããªãèŠåã3ã€ååšãããæåã«ãéåžžã«åçŽã ããå°ã®åæã¯çµåçã§ããå¿
èŠããããã€ãŸãã",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 7,
"tag": "p",
"text": "次ã«ãåã¯åææŒç®ã«ãããŠéããŠããªããã°ãªããªããããªãã¡ããã f : B â C {\\displaystyle f:B\\to C} ã〠g : A â B {\\displaystyle g:A\\to B} ãªãã°ã h = f â g {\\displaystyle h=f\\circ g} ã®ãããªå° h : A â C {\\displaystyle h:A\\to C} ããã®åã«ååšããªããã°ãªããªããæ¬¡ã®åã䜿ãã°ããããã©ã®ããã«åãããèŠãããšãã§ããã",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 8,
"tag": "p",
"text": "f ãš g ã¯ã©ã¡ããå°ã§ããã®ã§ãããããåæããããã®åã«ããããããã®å°ãåŸãã¯ãã§ãããã§ã¯ãã©ããå° f â g {\\displaystyle f\\circ g} ã ããã?å¯äžã®çã㯠i d A {\\displaystyle {\\mathit {id}}_{A}} ã§ãããåæ§ã« g â f = i d B {\\displaystyle g\\circ f={\\mathit {id}}_{B}} ããããã",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 9,
"tag": "p",
"text": "æåŸã«ããããªã察象 A ã«ã€ããŠãæçå° i d A : A â A {\\displaystyle {\\mathit {id}}_{A}:A\\to A} ãããªãã¡ãã®å°ãšã®åæãæçã§ãããããªå°ãå C ã«ååšããªããã°ãªããªããæ£ç¢ºã«èšãã°ãä»»æã®å° g : A â B {\\displaystyle g:A\\to B} ã«å¯ŸããŠ",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 10,
"tag": "p",
"text": "ã§ããã",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 11,
"tag": "p",
"text": "",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 12,
"tag": "p",
"text": "ãã®é
ç®ã§æã
ãèããããšããŠããäž»ãªåã¯ãHaskellã®åã察象ãšããHaskell ã®é¢æ°ãå°ãšããåæãšããŠ(.)ã䜿ãå Hask ã§ãããå A ãã Bã®é¢æ° f :: A -> B 㯠Hask ã®å°ã§ããã ãã®å®çŸ©ãæåã®2ã€ã®èŠåãæºããããšã¯å®¹æã«ç¢ºèªã§ããã ããªãã¡(.) ã¯çµåçã§ããããŸãä»»æã® f ãš gã«ã€ã㊠f . g ã¯æããã«äœããã®é¢æ°ã§ãããHask ã«ãããæçå°ã¯ id ã§ãããæ¬¡ã¯èªæã§ããã",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 13,
"tag": "p",
"text": "",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 14,
"tag": "p",
"text": "ãã ããããã¯æ·»ãåãæ¬ ããŠããŸã£ãŠãããäžèšã®èŠåã®å³å¯ãªç¿»èš³ã§ã¯ãªããHaskell ã®é¢æ° id 㯠å€çžçã§ãããããªãã¡ãã®å®çŸ©åãå€åã«ç°ãªãæ§ã
ãªåããšãããšãã§ããããããã¯åã§èšãæããã°ãç°ãªããœãŒã¹åã³ã¿ãŒã²ãããªããžã§ã¯ãããšãããšãã§ããããããåè«ã«ãããå°ã¯åçžçã§ãããããªãã¡ã©ããªå°ããœãŒã¹ãªããžã§ã¯ããšã¿ãŒã²ãããªããžã§ã¯ãã1ã€ãã€æå®ããŠå®çŸ©ããããå€çžãª Haskell 颿°ã¯ãã®åãæç€ºããããšã«ãã£ãŠåçžåããããšãã§ãã(åçžåã«ããã€ã³ã¹ã¿ã³ã¹å)ããããHaskåã®åAã«å¯Ÿããæçå°ã¯(id :: A -> A)ã§ããããšæžãã°ããæ£ç¢ºã«ãªãããããèæ
®ãããšãå
çšã®åã¯æ¬¡ã®ããã«æžãçŽããã",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 15,
"tag": "p",
"text": "",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 16,
"tag": "p",
"text": "ããããªããè°è«ãåçŽã«ãããããæå³ãæããã§ãããšãã¯ãã®éããç¡èŠããããšã«ããã",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 17,
"tag": "p",
"text": "",
"title": "åã®å°å
¥"
},
{
"paragraph_id": 18,
"tag": "p",
"text": "察象ãšå¯Ÿè±¡ãé¢é£ä»ããå°ãæã€å¹Ÿã€ãã®åãèŠãŠãããåè«ã®æ¬¡ã®å€§ããªè©±é¡ã¯åã©ãããé¢é£ã¥ãã颿(functorããã¡ã³ã¯ã¿)ã§ãããé¢æã®æ¬è³ªã¯åã®éã®å€æã§ãããã€ãŸãåC ãš Dãäžãããããšãã颿 F : C â D {\\displaystyle F:C\\to D} ã¯æ¬¡ã®ããšãããã",
"title": "颿"
},
{
"paragraph_id": 19,
"tag": "p",
"text": "颿ã®å¥œäŸã®ã²ãšã€ã¯å¿åŽé¢æ(forgetful functor) G r p â S e t {\\displaystyle \\mathbf {Grp} \\to \\mathbf {Set} } ã§ãããããã¯çŸ€ããã®å
åšããéåã«å¯Ÿå¿ä»ãã矀ã®å°ãåæ§ã«æ¯ãèããããã矀ã®ä»£ããã«éåã®äžã§å®çŸ©ããã颿°ã«å¯Ÿå¿ä»ãããä»ã®äŸãšããŠã¯åªéå颿 S e t â S e t {\\displaystyle \\mathbf {Set} \\to \\mathbf {Set} } ããããããã¯éåããã®åªéåã«å¯Ÿå¿ä»ãã颿° f : X â Y {\\displaystyle f:X\\to Y} ã颿° P ( X ) â P ( Y ) {\\displaystyle {\\mathcal {P}}(X)\\to {\\mathcal {P}}(Y)} ãã€ãŸã U â X {\\displaystyle U\\subset X} ããšã f ( U ) = { f ( u ) | u â U } {\\displaystyle f(U)=\\{\\,f(u)|u\\in U\\,\\}} ãšå®çŸ©ãããã f ã®äžã® U ã®åãè¿ã颿°ã«ãããã察å¿ä»ãããããããå C ã«ã€ããŠãCäžã®æç颿ãšããŠç¥ããã颿ãããªãã¡å¯Ÿè±¡ãå°ãããèªèº«ã«å¯Ÿå¿ä»ããã 1 C : C â C {\\displaystyle 1_{C}:C\\to C} ãå®çŸ©ã§ãããããã¯åŸã®ã¢ããåã®ç¯ã§äŸ¿å©ã§ããããšãããã«ãããã§ãããã",
"title": "颿"
},
{
"paragraph_id": 20,
"tag": "p",
"text": "颿ãåŸããªããã°ãªããªã幟ã€ãã®å
¬çãæããŠããããæåã«ãä»»æã®å¯Ÿè±¡ A äžã®æçå° i d A {\\displaystyle id_{A}} ã«ã€ããŠã F ( i d A ) {\\displaystyle F(id_{A})} ã¯æçå°ã§ãªããã°ãªããªãã",
"title": "颿"
},
{
"paragraph_id": 21,
"tag": "p",
"text": "",
"title": "颿"
},
{
"paragraph_id": 22,
"tag": "p",
"text": "ãµãã€ãã«ã颿ã¯å°ã®åæãåé
ããªããã°ãªããªãã",
"title": "颿"
},
{
"paragraph_id": 23,
"tag": "p",
"text": "Haskellã§ãç®ã«ããã£ãããšããããããããªãåã¯ã©ã¹ Functor ã¯ãå®éã«åè«ã«ãããé¢æã®æŠå¿µãšäžèŽããã颿ããµãã€ã®æ§æèŠçŽ ãããªãããšãæãåºããã颿ã¯ããåã®å¯Ÿè±¡ãå¥ã®åã®å¯Ÿè±¡ã«å¯Ÿå¿ä»ããæåã®åã®å°ããµãã€ãã®åã®å°ã«å¯Ÿå¿ä»ãããHaskell ã®é¢æã¯ Hask ãã funcã§ãããããã§ func ã¯é¢æã®åã®äžã§ã¡ããã©å®çŸ©ãããHaskã®éšååã§ãããäŸãã°ãªã¹ãé¢æã¯ Hask ãã Lstã§ãããããã§Lstã¯ãªã¹ãåãããªãã¡ä»»æã®åTã«å¯Ÿãããªã¹ãå[T]ã®ã¿ãå«ãåã§ãããLstã«ãããå°ã¯ãªã¹ãåã®äžã§å®çŸ©ããã颿°ã§ãããããã¯ä»»æã®åT, Uã«é¢ã㊠[T] -> [U]ã®é¢æ°ã§ãããã©ã®ããã«ããã Haskell ã®Functoråã¯ã©ã¹ãžãšçµã³ã€ãããããã®ã§ãããã?å®çŸ©ãæãåºããã",
"title": "颿"
},
{
"paragraph_id": 24,
"tag": "p",
"text": "ã€ã³ã¹ã¿ã³ã¹ã®äŸã瀺ããŠãããã",
"title": "颿"
},
{
"paragraph_id": 25,
"tag": "p",
"text": "ãããéµãšãªãéšåã§ãããåæ§ç¯å Maybe ã¯ä»»æã®å T ããšãæ°ããªåMaybe TãšãªãããŸããMaybe åãžãšçãããã fmap ã¯é¢æ° a -> b ããšã颿° Maybe a -> Maybe b ãè¿ãããŸãã«ããããŸãã«ããã§ã¯ãªãã!ãµãã€ã®æ§æèŠçŽ ãå®çŸ©ãããã²ãšã€ã¯Haskã®å¯Ÿè±¡ããšãå¥ã®å(ããã¯Maybeåã察象ãMaybeåäžã®é¢æ°ãå°ãšãã)ã®å¯Ÿè±¡ãè¿ãäœããããã²ãšã€ã¯Hask ã®å°ããšããã®åã®å°ãè¿ãäœããããã« Maybe ã¯é¢æã§ããã",
"title": "颿"
},
{
"paragraph_id": 26,
"tag": "p",
"text": "Haskellã®é¢æãå
容ã«é¢ããŠmapã§ãããããªåã衚ããšããããšã¯æçšãªçŽèгã§ãããããã¯ãªã¹ãã Maybeã ãã§ãªããæšã®ãããªããè€éãªæ§é ãããã§ãããæ§é ã®å
容ã«mapãè¡ã颿°ã¯fmapã䜿ã£ãŠæžãããšãã§ããã©ããªé¢ææ§é ããã®é¢æ°ã«æž¡ãããšãã§ãããäŸãã°ãData.List.map, Data.Map.map, Data.Array.IArray.amap ãªã©ããã¹ãŠãã«ããŒãããžã§ããªãã¯ãªé¢æ°ãæžãããšãã§ããã",
"title": "颿"
},
{
"paragraph_id": 27,
"tag": "p",
"text": "颿ã®å
¬çã¯ã©ãã ããã?ä»»æã®Aã«å¯Ÿãã i d A {\\displaystyle id_{A}} ãšããŠå€çžçãªé¢æ° id ã䜿ããæåã®åã¯æ¬¡ã®ããã«æžããã",
"title": "颿"
},
{
"paragraph_id": 28,
"tag": "p",
"text": "å
çšã®çŽèгã«ãããšããã®åŒã¯ãæ§é ã蟿ã£ãŠãããåèŠçŽ ã«äœãããªãmapãšãå
šãäœãããªãããšã¯çããããšè§£éã§ãããæ¬¡ã«ãå°ã®åæã¯åã« (.) ã§ãããã€ãŸãã",
"title": "颿"
},
{
"paragraph_id": 29,
"tag": "p",
"text": "ãã®ãµãã€ãã®åã¯å®çšçã«æ¥µããŠåœ¹ã«ç«ã€ã颿ããªã¹ããäœãã®ã³ã³ãããšèãããšãå³èŸºã¯2ãã¹ã®ã¢ã«ãŽãªãºã ã衚ããã€ãŸãæ§é ã«ã€ããŠãŸãgãmapããããã«fãmapããããã®é¢æã®å
¬çã¯ãã®ãããª2ãã¹ã®ã¢ã«ãŽãªãºã ãf . gãè¡ã1ãã¹ã®ã¢ã«ãŽãªãºã ãžãšå€æã§ããããšãä¿èšŒããããã®åŠç㯠èå(fusion)ãšããŠç¥ãããŠããã",
"title": "颿"
},
{
"paragraph_id": 30,
"tag": "p",
"text": "颿ã¯ã©ã®ããã«åè«ã Haskell ãžãšå€æããããã®è¯ãäŸãæäŸãããæ¬¡ãçè§£ã®éµãšãªãã",
"title": "颿"
},
{
"paragraph_id": 31,
"tag": "p",
"text": "",
"title": "颿"
},
{
"paragraph_id": 32,
"tag": "p",
"text": "",
"title": "颿"
},
{
"paragraph_id": 33,
"tag": "p",
"text": "ã¢ããã¯èšããŸã§ããªã Haskell ã®æ¥µããŠéèŠãªæŠå¿µã§ããããå®ã¯ãããã¯æ¬æ¥åè«ã«ç±æ¥ãããã®ã§ãããã¢ãã ã¯åããåãåãžã®é¢æã§ãããããã«ããã€ãã®è¿œå ã®æ§é ãæäŸãããã§ã¯å®çŸ©ãèŠãŠã¿ãããã¢ããã¯Cå
ã®ãã¹ãŠã®å¯Ÿè±¡ Xã«å¯ŸããŠãµãã€ã®å°ããšããªã颿 M : C â C {\\displaystyle M:C\\to C} ã§ããã",
"title": "ã¢ãã"
},
{
"paragraph_id": 34,
"tag": "p",
"text": "è°è«ãããŠããã¢ãããæãããªãšãããããã®é¢æ°ã«ã€ããŠäžæ·»å M ãçç¥ããããšã«ããåã«äœããã® X ã«å¯Ÿãã u n i t X {\\displaystyle {\\mathit {unit}}_{X}} ãš j o i n X {\\displaystyle {\\mathit {join}}_{X}} ã«ã€ããŠè¿°ã¹ãããšã«ããã",
"title": "ã¢ãã"
},
{
"paragraph_id": 35,
"tag": "p",
"text": "ã§ã¯ãã©ã®ããã«ããã Haskell ã®åã¯ã©ã¹ Monad ã«ç¿»èš³ãããããã¿ããã",
"title": "ã¢ãã"
},
{
"paragraph_id": 36,
"tag": "p",
"text": "ãã®ã¯ã©ã¹å¶çŽFunctor mã¯mããããããé¢æã®æ§é ãã€ãŸã察象ãšå°ã®å¯Ÿå¿ä»ããæã£ãŠããããšãä¿èšŒãããreturn ã¯å
šãŠã® X ã«å¯Ÿãã u n i t X {\\displaystyle {\\mathit {unit}}_{X}} ã®(å€çžçãª)é¡çŸ©èªã§ããããããããã«ã¯åé¡ããããreturnã®åã¯unitã«éåžžã«äŒŒãŠããããã©ããããäžæ¹ã®é¢æ°ããã°ãã°bindãšãåŒã°ãã (>>=)ã®åã¯joinã«äŒŒãŠããªããããã§ããã«å¥ã®ã¢ãã颿°join :: Monad m => m (m a) -> m aããããããã¯éåžžã«ãã䌌ãŠãããå®éã«ãjoin ãš (>>=)ã¯æ¬¡ã®ããã«äºãã«è¡šãããšãã§ããã",
"title": "ã¢ãã"
},
{
"paragraph_id": 37,
"tag": "p",
"text": "",
"title": "ã¢ãã"
},
{
"paragraph_id": 38,
"tag": "p",
"text": "ã€ãŸããã¢ããã® return, fmap, joinãå®çŸ©ããããšã¯ãreturn ãš (>>=)ãå®çŸ©ããããšãšåçã§ãããåè«ã§ã¢ããã®å®çŸ©ãããå
žåçãªæ¹æ³ãunit ãš joinãäžããããšã§ããã®ã«å¯ŸããŠãHaskell ããã°ã©ãã¯return ãš (>>=)ãäžããããšã奜ãããšãããããå€ãã®å Žåãåè«ã®æ¹æ³ã®ã»ããçã«ããªã£ãŠããã äœããã®æ§é M {\\displaystyle M} ããããä»»æã®å¯Ÿè±¡Xã M ( X ) {\\displaystyle M(X)} ãšãããã M ( M ( X ) ) {\\displaystyle M(M(X))} ã M ( X ) {\\displaystyle M(X)} ãšã§ããèªç¶ãªæ¹æ³ããããšããããã¯ãã°ãã°ã¢ããã§ãããæ¬¡ã®ç¯ã§äŸã瀺ãã",
"title": "ã¢ãã"
},
{
"paragraph_id": 39,
"tag": "p",
"text": "",
"title": "ã¢ãã"
},
{
"paragraph_id": 40,
"tag": "p",
"text": "å
ã»ã©è¿°ã¹ãåªéå颿 P : S e t â S e t {\\displaystyle P:\\mathbf {Set} \\to \\mathbf {Set} } ã¯ã¢ããããªããä»»æã®éåSã«ã€ããŠãèŠçŽ ããã®åéåãžåã u n i t S ( x ) = { x } {\\displaystyle {\\mathit {unit}}_{S}(x)=\\{x\\}} ãããããããã®åéåã®ããããã¯æããã« S ã®éšåéåã§ããããã£ãŠ u n i t S {\\displaystyle {\\mathit {unit}}_{S}} ã¯Sã®åªéåã®èŠçŽ ãè¿ããã€ãŸãã¢ããã®èŠæ±ãæºãããŠãããåæ§ã«é¢æ° j o i n S {\\displaystyle {\\mathit {join}}_{S}} ãæ¬¡ã®ããã«å®çŸ©ã§ãããåŒæ°ãšã㊠L â P ( P ( S ) ) {\\displaystyle L\\in {\\mathcal {P}}({\\mathcal {P}}(S))} ããšããããã¯ã",
"title": "ã¢ãã"
},
{
"paragraph_id": 41,
"tag": "p",
"text": "ãã£ãŠ j o i n S {\\displaystyle {\\mathit {join}}_{S}} ã¯ãããã®éšåéåã®åãè¿ãããšã§ãSã®ãŸãå¥ã®éšåéåãäžããããã«ãããåŒã§è¡šãã°ã",
"title": "ã¢ãã"
},
{
"paragraph_id": 42,
"tag": "p",
"text": "åŸã£ãŠã(次ã®ç¯ã§æ¢æ±ããèŠåãæºããããšã蚌æã§ããã°)P ã¯ã¢ããã§ããã",
"title": "ã¢ãã"
},
{
"paragraph_id": 43,
"tag": "p",
"text": "å®éã®ãšãããè°è«ã®å¯Ÿè±¡ãéåã®ä»£ããã«ãªã¹ãã«ãªããšããéããé€ãã°ãPã¯ã»ãšãã©ãªã¹ãã¢ãããšçããããããã¯ã»ãŒåããã®ã§ãããæ¯èŒããŠã¿ããã",
"title": "ã¢ãã"
},
{
"paragraph_id": 44,
"tag": "p",
"text": "",
"title": "ã¢ãã"
},
{
"paragraph_id": 45,
"tag": "p",
"text": "颿ãããåŒã°ããããã«ã¯åŸããªããã°ãªããªãå
¬çãããããã«ãã¢ããã«ã幟ã€ããã®ãããªå
¬çãååšããããŸãã¯ããããäžèЧããæ¬¡ã« Haskell ãžãšç¿»èš³ãããªããããéèŠãªã®ããã¿ãŠããããšã«ãããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 46,
"tag": "p",
"text": "ã¢ãã M : C â C {\\displaystyle M:C\\to C} ãšã A , B â C {\\displaystyle A,B\\in C} ã«å° f : A â B {\\displaystyle f:A\\to B} ããããšããã ãã®ãšã次ãæãç«ããªããŠã¯ãªããªãã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 47,
"tag": "p",
"text": "Haskell ãžã®ç¿»èš³ã¯ãªãã¹ãèªæã§ãã£ãŠã»ããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 48,
"tag": "p",
"text": "(fmap ãé¢æã®æ§æèŠçŽ ã®ã²ãšã€ã§ãå°ã«äœçšãããã®ã§ããããšãæãåºããã)ãããã®åã¯æåã¯å°ãäžå¯è§£ã«ãæããããã£ãããããã®åã¯ã©ãããæå³ã§ããªãã¢ããã¯ãããæºããã¹ããªã®ã ããã?ã§ã¯ãããã®æ³åã«ã€ããŠèª¿ã¹ãŠãããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 49,
"tag": "p",
"text": "join . fmap join = join . join",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 50,
"tag": "p",
"text": "ãã®èŠåãçè§£ããããã«ããŸãã¯ãªã¹ãã®äŸã䜿ã£ãŠããããæåã®èŠåã¯join . fmap join (巊蟺) ãš join . join (å³èŸº)ã®ãµãã€ã®é¢æ°ã«ã€ããŠè¿°ã¹ãŠããããããã®åã¯ã©ããªãã ããã?(ä»ã¯ãªã¹ãã¢ããã«ã€ããŠè°è«ããŠããã®ã§)joinã®åã¯[[a]] -> [a]ã§ããããšãæãåºãããã€ãŸã䞡蟺ã®åã¯ã©ã¡ãã[[[a]]] -> [a]ã§ããã(ãããåãã§ãããšããäºå®ã¯åœ¹ã«ç«ã€ãæçµçã«ã¯ã䞡蟺ãå
šãåã颿°ã§ããããšã瀺ãããšããŠããã®ã ã)ã§ã¯ããªã¹ãã®ãªã¹ãã®ãªã¹ãããããšãããã巊蟺ã¯ãã®äžéã®ãªã¹ãã« fmap joinãäœçšãã(1)ããã®çµæã« join ãé©çšãã(2)ã fmap ã¯ãªã¹ãã«å¯ŸããŠã¯ map ãšåãã§ããã®ã§ã(1)ã®èšç®ã¯ãŸããã¡ã°ãå€åŽã®ãªã¹ãã®èŠçŽ ã«å¯ŸããŠjoinãmapã§æœããåèŠçŽ ã«å¯ŸããŠãjoinã¯ãªã¹ãã®ãªã¹ããããããé£çµãããçµæãšããŠãªã¹ãã®ãªã¹ããåŸããããã(2)ã«ããããå
šäœã«joinãé©çšãããæçã«èšãã°ããããã¬ãã«ã«'å
¥ã蟌ã¿'ãäºçªç®ãšäžçªç®ã®ã¬ãã«ã朰ããŠã²ãšã€ã«ããŠã次ãã§ãããã¬ãã«ãšãã®æ°ããã¬ãã«ã朰ããŠã²ãšã€ã«ããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 51,
"tag": "p",
"text": "ã§ã¯å³èŸºã«ã€ããŠã¯ã©ãã ããã?æåã«ãªã¹ãã®ãªã¹ãã®ãªã¹ãã«å¯Ÿã㊠join ãå®è¡ãããæ®éjoinã¯äºéã®ãªã¹ãã«é©çšãããã®ã§ããããäžéã®ãªã¹ãã«ãé©çšã§ããããªããªãã[[[a]]]ã¯b = [a]ãšããã°[[b]]ãšæžããããã§ãããã€ãŸãäžéã®ãªã¹ãã¯ããæå³ã§äºéã®ãªã¹ãã«ãããªãããã ãææ·±éšã¯'ãã©ãã'ãªå€ã§ãªãå¥ã®ãªã¹ããããªã£ãŠãããã ãããããªã¹ãã®ãªã¹ã(ã®ãªã¹ã)ã«joinãé©çšãããšãå€åŽã®ãµãã€ã®ãªã¹ããã²ãšã€ã«å¹³åŠåããããå€ããäºçªç®ã®æ·±ãã®ãªã¹ãã®èŠçŽ ã¯ãã©ããã§ã¯ãªãäžçªç®ã®å±€ã®ãªã¹ããå«ãŸããŠããã®ã§ããã®çµæã¯ãªã¹ãã®ãªã¹ãã§ãããæ¬¡ã«ããäžæ¹ã®join ããã®æ§é ãå¹³åŠåãããèŠçŽãããšã巊蟺ã¯å
åŽã®ãµãã€ã®å±€ãæ°ããå±€ãžãšå¹³åŠåããããããæãå€åŽãšæ°ããå±€ãå¹³åŠåãããå³èŸºã¯å€åŽã®ãµãã€ã®å±€ããŸãå¹³åŠåããããããæ°ããå±€ãšæãå
åŽã®å±€ãå¹³åŠåããããããã®äºã€ã®æäœã¯çãããããã¯ããã°joinã«é¢ããçµååã®ãããªãã®ã§ããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 52,
"tag": "p",
"text": "次ã®ããã«ããMaybe ããŸãã¢ããã§ããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 53,
"tag": "p",
"text": "äžéã® Maybe (ããã¯Nothing, Just Nothing, Just (Just Nothing), Just (Just (Just x))ãšãã£ãå€ããšã)ãèããŠãäžã€ãã®èŠåã¯å
åŽã®ãµãã€ã®å±€ãå
ã«æœ°ããããããå€åŽã®å±€ã朰ãããšã¯ãå€åŽã®å±€ãå
ã«æœ°ããããããæãå
åŽã®å±€ã朰ãããšãšå
šãåãã§ãããšè¿°ã¹ãŠããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 54,
"tag": "p",
"text": "join . fmap return = join . return = id",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 55,
"tag": "p",
"text": "ããã§ã¯ãäºçªç®ã®æ³åã¯ã©ãã ããã?åã³ããªã¹ãã®äŸã§å§ããããäºçªç®ã®æ³åã§è¿°ã¹ãããŠãã䞡蟺㯠[a] -> [a]ã®é¢æ°ã§ããã巊蟺ã¯ãŸããªã¹ãã®ããããã®èŠçŽ xãèŠçŽ ãããã²ãšã€ã ãã®ãªã¹ã[x]ãžãšå€ããã·ã³ã°ã«ãã³ãªã¹ãã®ãªã¹ããåŸãããã®äºéã®ãªã¹ãã¯åã³joinã䜿ã£ãŠäžéã®ãªã¹ããžãšå¹³åŠåãããã以äžã巊蟺ã®è¡šã颿°ã§ãããäžæ¹å³èŸºã§ã¯ããªã¹ãå
šäœ[x, y, z, ...]ããšããããããªã¹ãã®ã·ã³ã°ã«ãã³ãªã¹ã[[x, y, z, ...]]ã«ããããããåã³ãã®ãµãã€ã®å±€ãã²ãšã€ã«å¹³åŠåããããã®èŠåã¯äžèšã§èª¬æã§ããã»ã©ã®èªæãã¯ãªãããreturnãã¢ããã®å€ã«é©çšããã®çµæãjoinããããšã¯ãreturnãæäžäœã®å±€ã®å
åŽã§å®è¡ããŠãå€åŽã§å®è¡ããŠãåãçµæã«ãªãã¹ãã§ãããšããããšãæ¬è³ªçã«è¿°ã¹ãŠããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 56,
"tag": "p",
"text": "",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 57,
"tag": "p",
"text": "return . f = fmap f . return",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 58,
"tag": "p",
"text": "join . fmap (fmap f) = fmap f . join",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 59,
"tag": "p",
"text": "æåŸã®ãµãã€ã®æ³åã¯ãã©ã®ããã«ã¢ãããæ¯èãã¹ããã«é¢ãããã£ãšèªæãªäºå®ã瀺ãããããã©ãçã§ãããã調ã¹ãæãç°¡åãªæ¹æ³ã¯ãå±éãã圢åŒã䜿ãããã«ããããå±éããããšã§ããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 60,
"tag": "p",
"text": "ã¢ãããåŸããªããã°ãªããªãèŠåã«ã€ããŠçŽèгçã«èª¬æãããã§ã¯ãªãããã¯éèŠãªã®ã?ãã®çã㯠do ãããã¯ã«ã€ããŠèãããšãã«æããã«ãªããæ¬¡ã®ã決ãŸãã®å€æã瀺ããŠããããã«ãdo ãããã¯ãæã®çµã¿åããã(>>=)ã䜿ããã«è¡šãããã®ãã ã®æ§æç³è¡£ã§ããããšãæãåºããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 61,
"tag": "p",
"text": "ããã§çšããŠãã4ã€ã®èŠåãããéåžžã® return ãš(>>=)ã䜿ã£ãã¢ããåã蚌æã§ããããšã«æ³šæãããã(éåžžã«å€§æãããªèšŒæãããã®ã§ãããã¯é£ã°ããŠããŸã£ãŠãæ§ããªãã)",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 62,
"tag": "p",
"text": "",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 63,
"tag": "p",
"text": "returnãš(>>=)ã䜿ããã®æ°ããªã¢ããåã¯ããããdoèšæ³ãžãšå€æã§ããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 64,
"tag": "p",
"text": "",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 65,
"tag": "p",
"text": "ã¢ããåã¯ããŸãdoãããã¯ãã©ã®ããã«æ©èœãã¹ãããšããåžžèãè¿°ã¹ãæã§ããããããããã®èŠåãã²ãšã€ã§ãç¡å¹ã§ããã°ãdoãããã¯ãæåŸ
ãããšããã«æäœã§ããªããªãã®ã§ãŠãŒã¶ãæ··ä¹±ãããèŠããã«ãã¢ããåã¯ãŠãŒã¶ããªãã£ã¬ã€ãã©ã€ã³ãªã®ã§ããã",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 66,
"tag": "p",
"text": "",
"title": "ã¢ããåãšãã®éèŠæ§"
},
{
"paragraph_id": 67,
"tag": "p",
"text": "ãã®ç« ã§é·ãéã®ãã蟿ã£ãŠãããåãšã¯äœããã©ããã£ãŠHaskellã«å¿çšãããã®ããèŠãŠããã颿ãã¯ãããšããåè«ã®åºæ¬çãªæŠå¿µãããã¢ããã®ãããªããçºå±çãªå
容ãŸã§ãããããããã«Haskellãããã«å¿
èŠäžå¯æ¬ ã§ãããã«ã€ããŠã玹ä»ããŠãããèªç¶å€æ(natural transformations)ãªã©ãæã
ã®ç®çã«å¿
èŠãªãã£ã幟ã€ãã®åè«ã®åºæ¬çäºé
ã«ã€ããŠã¯è§Šããªãã£ããã代ããã«Haskellã®æ§é ã®èåŸã«æ ¹ä»ãåè«ã®çŽèгçãªçè§£ãæäŸããã",
"title": "ãŸãšã"
},
{
"paragraph_id": 68,
"tag": "p",
"text": "",
"title": "ãŸãšã"
},
{
"paragraph_id": 69,
"tag": "p",
"text": "ãã³ãã¬ãŒã:Haskell navigation",
"title": "泚é"
}
] |
 ãã®é
ç®ã§ã¯ Haskell ã«é¢é£ããå
容ã«éã£ãŠåè«ã®æŠèгãäžããããšã詊ã¿ãããã®ããã«ãæ°åŠçãªå®çŸ©ã«äœµã㊠Haskell ã³ãŒãã瀺ãã絶察çãªå³å¯ãã¯æ±ããªãããã®ããããåè«ã®æŠå¿µãšã¯ã©ããªãã®ããã©ã®ããã« Haskell ã«é¢é£ãããã®çŽæçãªçè§£ãèªè
ã«äžããããšã远æ±ããã
|
{{Haskell minitoc|chapter=Wider Theory}}
ãã®é
ç®ã§ã¯ Haskell ã«é¢é£ããå
容ã«éã£ãŠåè«ã®æŠèгãäžããããšã詊ã¿ãããã®ããã«ãæ°åŠçãªå®çŸ©ã«äœµã㊠Haskell ã³ãŒãã瀺ãã絶察çãªå³å¯ãã¯æ±ããªãããã®ããããåè«ã®æŠå¿µãšã¯ã©ããªãã®ããã©ã®ããã« Haskell ã«é¢é£ãããã®çŽæçãªçè§£ãèªè
ã«äžããããšã远æ±ããã<!-- This article attempts to give an overview of category theory, in so far as it applies to Haskell. To this end, Haskell code will be given alongside the mathematical definitions. Absolute rigour is not followed; in its place, we seek to give the reader an intuitive feel for what the concepts of category theory are and how they relate to Haskell. -->
== åã®å°å
¥ <!-- Introduction to categories --> ==
[[Image:Simple-cat.png|left|frame|ïŒã€ã®å¯Ÿè±¡''A'', ''B'', ''C''ãïŒã€ã®æçå°<math>\mathit{id}_A</math>, <math>\mathit{id}_B</math>, <math>\mathit{id}_C</math>ãšãããã«å¥ã®å°<math>f : C \to B</math>, <math>g : A \to B</math>ãããªãåçŽãªåãïŒã€ãã®èŠçŽ (ã©ã®ããã«å°ãåæãããã®å®çŸ©)ã¯ç€ºããŠããªãã]]
<!-- [[Image:Simple-cat.png|left|frame|A simple category, with three objects ''A'', ''B'' and ''C'', three identity morphisms <math>\mathit{id}_A</math>, <math>\mathit{id}_B</math> and <math>\mathit{id}_C</math>, and two other morphisms <math>f : C \to B</math> and <math>g : A \to B</math>. The third element (the specification of how to compose the morphisms) is not shown.]] -->
æ¬è³ªçã«ãåãšã¯åçŽãªéãŸãã§ãããããã¯æ¬¡ã®ïŒã€ã®èŠçŽ ãããªãã
<!-- A category is, in essence, a simple collection. It has three components: -->
* '''察象'''(Object)ã®éãŸãã
* ãµãã€ã®å¯Ÿè±¡('''source object'''ãš'''target object''')ãã²ãšã€ã«çµã³ã€ãã'''å°'''ã®éãŸãã(ãããã¯'''arrow'''ãšåŒã°ããããšãããããHaskellã§ã¯ããã¯å¥ã®æå³ãæã€çšèªãªã®ã§ãããã§ã¯ãã®çšèªãé¿ããããšã«ããã) ''f'' ããœãŒã¹ãªããžã§ã¯ã ''A'' ããã¿ãŒã²ãããªããžã§ã¯ã ''B'' ãžã®å°ã§ãããšããããã <math>f : A \to B</math> ãšæžãã
* ãããã®å°ã®'''åæ'''ã®æŠå¿µã ''h'' ãå° ''f'', ''g'' ã®åæã§ãããšããããã <math>h = f \circ g</math> ãšæžãã
<!--
* A collection of '''objects'''.
* A collection of '''morphisms''', each of which ties two objects (a ''source object'' and a ''target object'') together. (These are sometimes called '''arrows''', but we avoid that term here as it has other connotations in Haskell.) If ''f'' is a morphism with source object ''A'' and target object ''B'', we write <math>f : A \to B</math>.
* A notion of '''composition''' of these morphisms. If ''h'' is the composition of morphisms ''f'' and ''g'', we write <math>h = f \circ g</math>. -->
æ§ã
ãªãã®ãåãã€ãããäŸãã°ã'''Set''' ã¯å
šãŠã®éåã察象ãšããå°ãšããŠæšæºçãªé¢æ°ãåæãšããŠéåžžã®é¢æ°åæãæã€åã§ããã(åã®ååã¯ãã°ãã°å€ªåã§è¡šãããã)'''Grp'''ã¯å
šãŠã®çŸ€ã察象ãšããå°ãšããŠçŸ€ã®æŒç®ãä¿åãã颿°(矀æºåå)ãæã€åã§ãããã€ãŸããä»»æã®2ã€ã®çŸ€ ''G'', ''H'' (ããããæŒç®<math>*</math>, <math> \cdot </math>ããã€)ã«ã€ããŠã
<math>f(u * v) = f(u) \cdot f(v)</math>ãªãã°ããã€ãã®ãšãã«éãã<math>f : G \to H</math> 㯠'''Grp''' å
ã®å°ã§ããã
<!-- Lots of things form categories. For example, '''Set''' is the category of all sets with morphisms as standard functions and composition being standard function composition. (Category names are often typeset in bold face.) '''Grp''' is the category of all groups with morphisms as functions that preserve group operations (the group homomorphisms), i.e. for any two groups ''G'' with operation ''*'' and ''H'' with operation ''·'', a function <math>f : G \to H</math> is a morphism in '''Grp''' iff:
: <math>f(u * v) = f(u) \cdot f(v)</math> -->
å°ã¯ãã€ã颿°ã®ããã«ãæããããããã§ããå¿
èŠã¯ãªããäŸãã°ããããªãåé åº (''P'', <math>\leq</math>)ãåãå®çŸ©ãããããã§å¯Ÿè±¡ã¯''P''ã®èŠçŽ ã§ãããä»»æã®2ã€ã®å¯Ÿè±¡''A'', ''B''ã«ã€ããŠ<math>A \leq B</math>ã§ãããšããã€ãã®ãšãã«éã''A''ãš''B''ã®éã«å°ãååšããããŸããè€æ°ã®ç°ãªãå°ãåããœãŒã¹ãªããžã§ã¯ããšã¿ãŒã²ãããªããžã§ã¯ããæã€ããšãã§ããã'''Set'''ã®äŸã§ããã°ã<math>\sin</math> ãš <math>\cos</math> ã¯ãããããœãŒã¹ãªããžã§ã¯ã<math>\mathbb{R}</math> ãš ã¿ãŒã²ãããªããžã§ã¯ã <math>[-1,1]</math>ããã€ãããã¡ãããããã¯åãå°ã§ã¯ãªãïŒ
<!-- It may seem that morphisms are always functions, but this needn't be the case. For example, any partial order (''P'', <math>\leq</math>) defines a category where the objects are the elements of ''P'', and there is a morphism between any two objects ''A'' and ''B'' iff <math>A \leq B</math>. Moreover, there are allowed to be multiple morphisms with the same source and target objects; using the '''Set''' example, <math>\sin</math> and <math>\cos</math> are both functions with source object <math>\mathbb{R}</math> and target object <math>[-1,1]</math>, but theyâre most certainly not the same morphism! -->
=== ã«ããŽãªå <!-- Category laws --> ===
åãåŸããªããã°ãªããªãèŠåãïŒã€ååšãããæåã«ãéåžžã«åçŽã ããå°ã®åæã¯'''''çµåç'''''ã§ããå¿
èŠããããã€ãŸãã
: <math>f \circ (g \circ h) = (f \circ g) \circ h</math>
次ã«ãåã¯åææŒç®ã«ãããŠ'''éããŠ'''ããªããã°ãªããªããããªãã¡ããã<math>f : B \to C</math> ã〠<math>g : A \to B</math>ãªãã°ã<math>h = f \circ g</math>ã®ãããªå°<math>h : A \to C</math>ããã®åã«ååšããªããã°ãªããªããæ¬¡ã®åã䜿ãã°ããããã©ã®ããã«åãããèŠãããšãã§ããã
[[Image:Composition-ex.png|center]]
''f'' ãš ''g'' ã¯ã©ã¡ããå°ã§ããã®ã§ãããããåæããããã®åã«ããããããã®å°ãåŸãã¯ãã§ãããã§ã¯ãã©ããå°<math>f \circ g</math>ã ãããïŒå¯äžã®çãã¯<math>\mathit{id}_A</math>ã§ãããåæ§ã«<math>g \circ f = \mathit{id}_B</math>ããããã
æåŸã«ããããªã察象 ''A'' ã«ã€ããŠã'''''æç'''''å°<math>\mathit{id}_A : A \to A</math>ãããªãã¡ãã®å°ãšã®åæãæçã§ãããããªå°ãå ''C'' ã«ååšããªããã°ãªããªããæ£ç¢ºã«èšãã°ãä»»æã®å° <math>g : A \to B</math> ã«å¯ŸããŠ
: <math>g \circ \mathit{id}_A = \mathit{id}_B \circ g = g</math>
ã§ããã
<!-- There are three laws that categories need to follow. Firstly, and most simply, the composition of morphisms needs to be '''''associative'''''. Symbolically,
: <math>f \circ (g \circ h) = (f \circ g) \circ h</math>
Secondly, the category needs to be '''''closed''''' under the composition operation. So if <math>f : B \to C</math> and <math>g : A \to B</math>, then there must be some morphism <math>h : A \to C</math> in the category such that <math>h = f \circ g</math>. We can see how this works using the following category:
[[Image:Composition-ex.png|center]]
''f'' and ''g'' are both morphisms so we must be able to compose them and get another morphism in the category. So which is the morphism <math>f \circ g</math>? The only option is <math>\mathit{id}_A</math>. Similarly, we see that <math>g \circ f = \mathit{id}_B</math>.
Lastly, given a category ''C'' there needs to be for every object <code>A</code> an '''''identity''' morphism'', <math>\mathit{id}_A : A \to A</math> that is an identity of composition with other morphisms. Put precisely, for every morphism <math>g : A \to B</math>:
: <math>g \circ \mathit{id}_A = \mathit{id}_B \circ g = g</math> -->
=== Haskell ã®å '''Hask''' <!-- '''Hask''', the Haskell category --> ===
ãã®é
ç®ã§æã
ãèããããšããŠããäž»ãªåã¯ãHaskellã®åã察象ãšããHaskell ã®é¢æ°ãå°ãšããåæãšããŠ<code>(.)</code>ã䜿ãå '''Hask''' ã§ãããå <code>A</code> ãã <code>B</code>ã®é¢æ° <code>f :: A -> B</code> 㯠'''Hask''' ã®å°ã§ããã
ãã®å®çŸ©ãæåã®2ã€ã®èŠåãæºããããšã¯å®¹æã«ç¢ºèªã§ããã
ããªãã¡<code>(.)</code> ã¯çµåçã§ããããŸãä»»æã® <code>f</code> ãš <code>g</code>ã«ã€ã㊠<code>f . g</code> ã¯æããã«äœããã®é¢æ°ã§ããã'''Hask''' ã«ãããæçå°ã¯ <code>id</code> ã§ãããæ¬¡ã¯èªæã§ããã
<ref>å®ã¯ããã«ã¯åŸ®åŠãªéšåãååšããã<code>(.)</code>ã¯é
å»¶è©äŸ¡é¢æ°ã§ããããããã<code>f</code> ã <code>undefined</code>ã§ãããš<code>id . f = \_ -> _|_</code>ãšãªããããŠãå
šãŠã®æå³ãšç®çã«ãããŠããã¯<code>_|_</code>ãšçããããã«èŠãããããããªãããå®ã¯æ£æ Œå颿°<code>seq</code>ã䜿ãããšã§ããããåºå¥ããããšãã§ãããããã¯åã®æåŸã®èŠåãç Žãããããšãæå³ãããæ°ãã«æ£æ Œãªåæé¢æ°<code>f .! g = ((.) $! f) $! g</code>ãå®çŸ©ããã°'''Hask'''ãæ£ããåã«ããããšãã§ããããããããã§ã¯æ®éã®<code>(.)</code>ã䜿ã£ãŠé²ããŠããããšã«ãããå
šãŠã®ççŸã¯
<code>seq</code>ãè¯ãèšèªã®æ§è³ªãã²ã©ãç Žå£ãããšããããšã®ããã«ããŠããã</ref>
<!-- The main category weâll be concerning ourselves with in this article is '''Hask''', the category of Haskell types and Haskell functions as morphisms, using <code>(.)</code> for composition: a function <code>f :: A -> B</code> for types <code>A</code> and <code>B</code> is a morphism in '''Hask'''. We can check the first and second law easily: we know <code>(.)</code> is an associative function, and clearly, for any <code>f</code> and <code>g</code>, <code>f . g</code> is another function. In '''Hask''', the identity morphism is <code>id</code>, and we have trivially: -->
: <code>id . f = f . id = f</code>
<!-- <ref>Actually, there is a subtlety here: because <code>(.)</code> is a lazy function, if <code>f</code> is <code>undefined</code>, we have that <code>id . f = \_ -> _|_</code>. Now, while this may seem equivalent to <code>_|_</code> for all intents and purposes, you can actually tell them apart using the strictifying function <code>seq</code>, meaning that the last category law is broken. We can define a new strict composition function, <code>f .! g = ((.) $! f) $! g</code>, that makes '''Hask''' a category. We proceed by using the normal <code>(.)</code>, though, and attribute any discrepancies to the fact that <code>seq</code> breaks an awful lot of the nice language properties anyway.</ref> -->
ãã ããããã¯æ·»ãåãæ¬ ããŠããŸã£ãŠãããäžèšã®èŠåã®å³å¯ãªç¿»èš³ã§ã¯ãªããHaskell ã®é¢æ° <code>id</code> 㯠''å€çžç''ã§ãããããªãã¡ãã®å®çŸ©åãå€åã«ç°ãªãæ§ã
ãªåããšãããšãã§ããããããã¯åã§èšãæããã°ãç°ãªããœãŒã¹åã³ã¿ãŒã²ãããªããžã§ã¯ãããšãããšãã§ããããããåè«ã«ãããå°ã¯''åçžç''ã§ãããããªãã¡ã©ããªå°ããœãŒã¹ãªããžã§ã¯ããšã¿ãŒã²ãããªããžã§ã¯ãã1ã€ãã€æå®ããŠå®çŸ©ããããå€çžãª Haskell 颿°ã¯ãã®åãæç€ºããããšã«ãã£ãŠåçžåããããšãã§ãã(åçžåã«ãã''ã€ã³ã¹ã¿ã³ã¹å'')ãããã'''Hask'''åã®å<code>A</code>ã«å¯Ÿããæçå°ã¯<code>(id :: A -> A)</code>ã§ããããšæžãã°ããæ£ç¢ºã«ãªãããããèæ
®ãããšãå
çšã®åã¯æ¬¡ã®ããã«æžãçŽããã
<!-- This isn't an exact translation of the law above, though; weâre missing subscripts. The function <code>id</code> in Haskell is ''polymorphic'' - it can take many different types for its domain and range, or, in category-speak, can have many different source and target objects. But morphisms in category theory are by definition ''monomorphic'' - each morphism has one specific source object and one specific target object. A polymorphic Haskell function can be made monomorphic by specifying its type (''instantiating'' with a monomorphic type), so it would be more precise if we said that the identity morphism from '''Hask''' on a type <code>A</code> is <code>(id :: A -> A)</code>. With this in mind, the above law would be rewritten as: -->
: <code>(id :: B -> B) . f = f . (id :: A -> A) = f</code>
ããããªããè°è«ãåçŽã«ãããããæå³ãæããã§ãããšãã¯ãã®éããç¡èŠããããšã«ããã
<!-- However, for simplicity, we will ignore this distinction when the meaning is clear. -->
{{Exercises|
*ããã»ã©è§Šãããšãããä»»æã®åé åº (''P'', <math>\leq</math>) ã¯''P''ã®èŠçŽ ã察象ãèŠçŽ ''a'' ãš ''b'' ã«ã€ã㊠a <math>\leq</math> b ã§ãããšããã€ãã®ãšãã«éã''a, b''éã«å°ããã€åã§ãããäžèšã®èŠåã®ã©ãããã®<math>\leq</math>ã®æšç§»æ§ãä¿èšŒããŠãããïŒ
*(é£ãã) ããäžèšã®äŸã«å¥ã®å°ãä»ãè¶³ããšããã¯åã§ã¯ãªããªãããªããïŒãã³ãïŒåææŒç®ã®çµåæ§ãèããŠã¿ãã[[Image:Not-a-cat.png|center]]}}
<!-- {{Exercises|
* As was mentioned, any partial order (''P'', <math>\leq</math>) is a category with objects as the elements of ''P'' and a morphism between elements ''a'' and ''b'' iff a <math>\leq</math> b. Which of the above laws guarantees the transitivity of <math>\leq</math>?
* (Harder.) If we add another morphism to the above example, it fails to be a category. Why? Hint: think about associativity of the composition operation.
[[Image:Not-a-cat.png|center]]}} -->
== 颿 <!-- Functors --> ==
[[Image:Functor.png|frame|right|ãµãã€ã®å<math>\mathbf{C}</math> ãš <math>\mathbf{D}</math> ã®éã®é¢æã察象ã®å¯Ÿå¿ã¯é»è²ã®ãå°ã®å¯Ÿå¿ã¯éè²ã®ç Žç·ç¢å°ã§ç€ºãããæ³šç®ãã¹ãã¯å¯Ÿè±¡ ''A'' ãšå¯Ÿè±¡ ''B''ã®äž¡æ¹ã <math>\mathbf{D}</math> ã®åã察象ã«å¯Ÿå¿ä»ããããŠããããšã§ããããããã ''g'' ã¯ãœãŒã¹ãšã¿ãŒã²ãããåã察象ã§ããå°ã«å€æãã(ããã¯æçå°ã§ããå¿
èŠã¯ãªã)ã<math>id_A</math> ãš <math>id_B</math>ã¯åãå°ãšãªãã]]
<!--
[[Image:Functor.png|frame|right|A functor between two categories, <math>\mathbf{C}</math> and <math>\mathbf{D}</math>. Of note is that the objects ''A'' and ''B'' both get mapped to the same object in <math>\mathbf{D}</math>, and that therefore ''g'' becomes a morphism with the same source and target object (but isn't necessarily an identity), and <math>id_A</math> and <math>id_B</math> become the same morphism. The arrows showing the mapping of objects are shown in a dotted, pale olive. The arrows showing the mapping of morphisms are shown in a dotted, pale blue.]] -->
察象ãšå¯Ÿè±¡ãé¢é£ä»ããå°ãæã€å¹Ÿã€ãã®åãèŠãŠãããåè«ã®æ¬¡ã®å€§ããªè©±é¡ã¯åã©ãããé¢é£ã¥ãã'''颿'''(functorããã¡ã³ã¯ã¿)ã§ãããé¢æã®æ¬è³ªã¯åã®éã®å€æã§ãããã€ãŸãå''C'' ãš ''D''ãäžãããããšãã颿 <math>F : C \to D</math>ã¯æ¬¡ã®ããšãããã
<!-- So we have some categories which have objects and morphisms that relate our objects together. The next Big Topic in category theory is the '''functor''', which relates categories together. A functor is essentially a transformation between categories, so given categories ''C'' and ''D'', a functor <math>F : C \to D</math>: -->
* ''C'' å
ã®ãããã察象 ''A''ãã''D''å
ã®<math>F(A)</math>ã«å¯Ÿå¿ä»ãã
* ''C'' å
ã®å° <math>f : A \to B</math> ã ''D'' å
ã® <math>F(f) : F(A) \to F(B)</math> ã«å¯Ÿå¿ä»ãã
<!-- * Maps any object ''A'' in ''C'' to <math>F(A)</math>, in ''D''.
* Maps morphisms <math>f : A \to B</math> in ''C'' to <math>F(f) : F(A) \to F(B)</math> in ''D''. -->
颿ã®å¥œäŸã®ã²ãšã€ã¯å¿åŽé¢æ(forgetful functor) <math>\mathbf{Grp} \to \mathbf{Set}</math> ã§ãããããã¯çŸ€ããã®å
åšããéåã«å¯Ÿå¿ä»ãã矀ã®å°ãåæ§ã«æ¯ãèããããã矀ã®ä»£ããã«éåã®äžã§å®çŸ©ããã颿°ã«å¯Ÿå¿ä»ãããä»ã®äŸãšããŠã¯åªéå颿 <math>\mathbf{Set} \to \mathbf{Set}</math> ããããããã¯éåããã®åªéåã«å¯Ÿå¿ä»ãã颿° <math>f : X \to Y</math> ã颿° <math>\mathcal{P}(X) \to \mathcal{P}(Y)</math>ãã€ãŸã <math>U \subset X</math> ããšã <math>f(U) = \{ \, f(u) | u \in U \, \}</math> ãšå®çŸ©ãããã ''f'' ã®äžã® ''U'' ã®åãè¿ã颿°ã«ãããã察å¿ä»ãããããããå ''C'' ã«ã€ããŠã''C''äžã®æç颿ãšããŠç¥ããã颿ãããªãã¡å¯Ÿè±¡ãå°ãããèªèº«ã«å¯Ÿå¿ä»ããã<math>1_C : C \to C</math>ãå®çŸ©ã§ãããããã¯åŸã®[[#ã¢ããåãšãã®éèŠæ§|ã¢ããå]]ã®ç¯ã§äŸ¿å©ã§ããããšãããã«ãããã§ããããã
<!-- One of the canonical examples of a functor is the forgetful functor <math>\mathbf{Grp} \to \mathbf{Set}</math> which maps groups to their underlying sets and group morphisms to the functions which behave the same but are defined on sets instead of groups. Another example is the power set functor <math>\mathbf{Set} \to \mathbf{Set}</math> which maps sets to their power sets and maps functions <math>f : X \to Y</math> to functions <math>\mathcal{P}(X) \to \mathcal{P}(Y)</math> which take inputs <math>U \subset X</math> and return <math>f(U)</math>, the image of ''U'' under ''f'', defined by <math>f(U) = \{ \, f(u) : u \in U \, \}</math>. For any category ''C'', we can define a functor known as the identity functor on ''C'', or <math>1_C : C \to C</math>, that just maps objects to themselves and morphisms to themselves. This will turn out to be useful in the [[#The monad laws and their importance|monad laws]] section later on. -->
颿ãåŸããªããã°ãªããªã幟ã€ãã®å
¬çãæããŠããããæåã«ãä»»æã®å¯Ÿè±¡ ''A'' äžã®æçå° <math>id_A</math> ã«ã€ããŠã<math>F(id_A)</math> ã¯æçå°ã§ãªããã°ãªããªãã
<!-- Once again there are a few axioms that functors have to obey. Firstly, given an identity morphism <math>id_A</math> on an object ''A'', <math>F(id_A)</math> must be the identity morphism on <math>F(A)</math>, i.e.: -->
: <math>F(id_A) = id_{F(A)}</math>
ãµãã€ãã«ã颿ã¯å°ã®åæãåé
ããªããã°ãªããªãã
<!-- Secondly functors must distribute over morphism composition, i.e. -->
: <math>F(f \circ g) = F(f) \circ F(g)</math>
{{Exercises|å³ã®å³ã«ãããŠã颿ã®èŠåãæãç«ã£ãŠãããšã確ãããã}}
<!-- {{Exercises|For the diagram given on the right, check these functor laws.}} -->
=== '''Hask'''ã«ããã颿 <!-- Functors on '''Hask''' --> ===
Haskellã§ãç®ã«ããã£ãããšããããããããªãåã¯ã©ã¹ Functor ã¯ãå®éã«åè«ã«ãããé¢æã®æŠå¿µãšäžèŽããã颿ããµãã€ã®æ§æèŠçŽ ãããªãããšãæãåºããã颿ã¯ããåã®å¯Ÿè±¡ãå¥ã®åã®å¯Ÿè±¡ã«å¯Ÿå¿ä»ããæåã®åã®å°ããµãã€ãã®åã®å°ã«å¯Ÿå¿ä»ãããHaskell ã®é¢æã¯ '''Hask''' ãã ''func''ã§ãããããã§ ''func'' ã¯é¢æã®åã®äžã§ã¡ããã©å®çŸ©ããã''Hask''ã®éšååã§ãããäŸãã°ãªã¹ãé¢æã¯ '''Hask''' ãã '''Lst'''ã§ãããããã§'''Lst'''ã¯''ãªã¹ãå''ãããªãã¡ä»»æã®å<code>T</code>ã«å¯Ÿãããªã¹ãå<code>[T]</code>ã®ã¿ãå«ãåã§ããã'''Lst'''ã«ãããå°ã¯ãªã¹ãåã®äžã§å®çŸ©ããã颿°ã§ãããããã¯ä»»æã®å<code>T</code>, <code>U</code>ã«é¢ã㊠<code>[T] -> [U]</code>ã®é¢æ°ã§ãããã©ã®ããã«ããã Haskell ã®Functoråã¯ã©ã¹ãžãšçµã³ã€ãããããã®ã§ããããïŒå®çŸ©ãæãåºããã
<!-- The Functor typeclass you will probably have seen in Haskell does in fact tie in with the categorical notion of a functor. Remember that a functor has two parts: it maps objects in one category to objects in another and morphisms in the first category to morphisms in the second. Functors in Haskell are from '''Hask''' to ''func'', where ''func'' is the subcategory of '''Hask''' defined on just that functor's types. E.g. the list functor goes from '''Hask''' to '''Lst''', where '''Lst''' is the category containing only ''list types'', that is, <code>[T]</code> for any type <code>T</code>. The morphisms in '''Lst''' are functions defined on list types, that is, functions <code>[T] -> [U]</code> for types <code>T</code>, <code>U</code>. How does this tie into the Haskell typeclass Functor? Recall its definition: -->
class Functor (f :: * -> *) where
fmap :: (a -> b) -> (f a -> f b)
ã€ã³ã¹ã¿ã³ã¹ã®äŸã瀺ããŠãããã
<!-- Let's have a sample instance, too: -->
instance Functor Maybe where
fmap f (Just x) = Just (f x)
fmap _ Nothing = Nothing
ãããéµãšãªãéšåã§ããã''åæ§ç¯å'' Maybe ã¯ä»»æã®å <code>T</code> ããšãæ°ããªå<code>Maybe T</code>ãšãªãããŸããMaybe åãžãšçãããã <code>fmap</code> ã¯é¢æ° <code>a -> b</code> ããšã颿° <code>Maybe a -> Maybe b</code> ãè¿ãããŸãã«ããããŸãã«ããã§ã¯ãªããïŒãµãã€ã®æ§æèŠçŽ ãå®çŸ©ãããã²ãšã€ã¯'''Hask'''ã®å¯Ÿè±¡ããšãå¥ã®å(ããã¯Maybeåã察象ãMaybeåäžã®é¢æ°ãå°ãšãã)ã®å¯Ÿè±¡ãè¿ãäœããããã²ãšã€ã¯'''Hask''' ã®å°ããšããã®åã®å°ãè¿ãäœããããã« Maybe ã¯é¢æã§ããã
<!-- Here's the key part: the ''type constructor'' Maybe takes any type <code>T</code> to a new type, <code>Maybe T</code>. Also, <code>fmap</code> restricted to Maybe types takes a function <code>a -> b</code> to a function <code>Maybe a -> Maybe b</code>. But that's it! We've defined two parts, something that takes objects in '''Hask''' to objects in another category (that of Maybe types and functions defined on Maybe types), and something that takes morphisms in '''Hask''' to morphisms in this category. So Maybe is a functor. -->
Haskellã®é¢æãå
容ã«é¢ããŠmapã§ãããããªåã衚ããšããããšã¯æçšãªçŽèгã§ãããããã¯ãªã¹ãã Maybeã ãã§ãªããæšã®ãããªããè€éãªæ§é ãããã§ãããæ§é ã®å
容ã«mapãè¡ã颿°ã¯<code>fmap</code>ã䜿ã£ãŠæžãããšãã§ããã©ããªé¢ææ§é ããã®é¢æ°ã«æž¡ãããšãã§ãããäŸãã°ãData.List.map, Data.Map.map, Data.Array.IArray.amap ãªã©ããã¹ãŠãã«ããŒãããžã§ããªãã¯ãªé¢æ°ãæžãããšãã§ããã
<!-- A useful intuition regarding Haskell functors is that they represent types that can be mapped over. This could be a list or a Maybe, but also more complicated structures like trees. A function that does some mapping could be written using <code>fmap</code>, then any functor structure could be passed into this function. E.g. you could write a generic function that covers all of Data.List.map, Data.Map.map, Data.Array.IArray.amap, and so on. -->
颿ã®å
¬çã¯ã©ãã ãããïŒä»»æã®''A''ã«å¯Ÿãã<math>id_A</math> ãšããŠå€çžçãªé¢æ° <code>id</code> ã䜿ããæåã®åã¯æ¬¡ã®ããã«æžããã
<!-- What about the functor axioms? The polymorphic function <code>id</code> takes the place of <math>id_A</math> for any ''A'', so the first law states: -->
fmap id = id
å
çšã®çŽèгã«ãããšããã®åŒã¯ãæ§é ã蟿ã£ãŠãããåèŠçŽ ã«äœãããªãmapãšãå
šãäœãããªãããšã¯çããããšè§£éã§ãããæ¬¡ã«ãå°ã®åæã¯åã« <code>(.)</code> ã§ãããã€ãŸãã
<!-- With our above intuition in mind, this states that mapping over a structure doing nothing to each element is equivalent to doing nothing overall. Secondly, morphism composition is just <code>(.)</code>, so -->
fmap (f . g) = fmap f . fmap g
ãã®ãµãã€ãã®åã¯å®çšçã«æ¥µããŠåœ¹ã«ç«ã€ã颿ããªã¹ããäœãã®ã³ã³ãããšèãããšãå³èŸºã¯ïŒãã¹ã®ã¢ã«ãŽãªãºã ã衚ããã€ãŸãæ§é ã«ã€ããŠãŸã<code>g</code>ãmapããããã«<code>f</code>ãmapããããã®é¢æã®å
¬çã¯ãã®ãããª2ãã¹ã®ã¢ã«ãŽãªãºã ã<code>f . g</code>ãè¡ãïŒãã¹ã®ã¢ã«ãŽãªãºã ãžãšå€æã§ããããšãä¿èšŒããããã®åŠç㯠''èå''(fusion)ãšããŠç¥ãããŠããã
<!-- This second law is very useful in practice. Picturing the functor as a list or similar container, the right-hand side is a two-pass algorithm: we map over the structure, performing <code>g</code>, then map over it again, performing <code>f</code>. The functor axioms guarantee we can transform this into a single-pass algorithm that performs <code>f . g</code>. This is a process known as ''fusion''. -->
{{Exercises|ãªã¹ãé¢æãš Maybe 颿ã«ã€ããŠããããã®èŠåã確ãããã}}
<!-- {{Exercises|Check the laws for the Maybe and list functors.}} -->
=== åè«ã®æŠå¿µãã Haskellãžã®å€æ <!-- Translating categorical concepts into Haskell --> ===
颿ã¯ã©ã®ããã«åè«ã Haskell ãžãšå€æããããã®è¯ãäŸãæäŸãããæ¬¡ãçè§£ã®éµãšãªãã
<!-- Functors provide a good example of how category theory gets translated into Haskell. The key points to remember are that: -->
* å '''Hask''' ãšãã®éšååãæ±ãã
* 察象ã¯åã§ããã
* å°ã¯é¢æ°ã§ããã
* åãåãå¥ã®åãè¿ããã®ãåæ§æåã§ããã
* 颿°ããšãå¥ã®é¢æ°ãè¿ããã®ãé«é颿°ã§ããã
* åè«ã§ã¯ãã°ãã°äžåºŠã«å€ãã®å¯Ÿè±¡ã«ããã£ãŠç©äºãå®çŸ©ããããšããäºå®ããåã¯ã©ã¹ãšãããåæã«æäŸããå€çžæ§ã¯ããŸãæããŠããã
<!--
* We work in the category '''Hask''' and its subcategories.
* Objects are types.
* Morphisms are functions.
* Things that take a type and return another type are type constructors.
* Things that take a function and return another function are higher-order functions.
* Typeclasses, along with the polymorphism they provide, make a nice way of capturing the fact that in category theory things are often defined over a number of objects at once.
-->
== ã¢ãã <!-- Monads --> ==
[[Image:Unit-join.png|frame|right|ã¢ããã®å
šãŠã®å¯Ÿè±¡ã«ã€ããŠ''unit'' ãš ''join''ã®ãµãã€ã®å°ãååšããªããŠã¯ãªããªãã]]
<!-- [[Image:Unit-join.png|frame|right|''unit'' and ''join'', the two morphisms that must exist for every object for a given monad.]] -->
ã¢ããã¯èšããŸã§ããªã Haskell ã®æ¥µããŠéèŠãªæŠå¿µã§ããããå®ã¯ãããã¯æ¬æ¥åè«ã«ç±æ¥ãããã®ã§ããã''ã¢ãã'' ã¯åããåãåãžã®é¢æã§ãããããã«ããã€ãã®è¿œå ã®æ§é ãæäŸãããã§ã¯å®çŸ©ãèŠãŠã¿ãããã¢ããã¯''C''å
ã®ãã¹ãŠã®å¯Ÿè±¡ ''X''ã«å¯ŸããŠãµãã€ã®å°ããšããªã颿 <math>M : C \to C</math> ã§ãã<ref>çéããåè«ã®çè«å®¶ã¯ãããã§å°ãåçŽåããŠããããšã«æ°ä»ãã ããã''unit''ãš''join''ãèªç¶å€æ(natural transformations)ãšããŠå°å
¥ãã代ããã«ãããããæç€ºçã«å°ãšããŠæ±ã£ãããããŠnaturalityãã¢ããåã®[[#ïŒçªç®ãšïŒçªç®ã®èŠå|èŠåïŒãšèŠåïŒ]]ãšããŠè¿œå ãããããã§ã¯åè«å
šäœãæããããšããŠããããã§ã¯ãªããHaskellã®ããæ§é ã«å¯Ÿããçè«çè£ä»ããšããŠã®åè«ã ãã瀺ãããããã«ããã®ãããªåçŽåãè¡ã£ãããããã®å°ã«Haskellã§å¯Ÿå¿ãããã®ã飿³ãããååãäžããŠããããšã«æ°ä»ãèªè
ãããããç¥ããªããããã¯åå<math>\eta</math> ãš <math>\mu</math>ãçŽæçã§ãªãããã§ããã</ref>ã
<!-- Monads are obviously an extremely important concept in Haskell, and in fact they originally came from category theory. A ''monad'' is a special type of functor, from a category to that same category, that supports some additional structure. So, down to definitions. A monad is a functor <math>M : C \to C</math>, along with two morphisms<ref>Experienced category theorists will notice that we're simplifying things a bit here; instead of presenting ''unit'' and ''join'' as natural transformations, we treat them explicitly as morphisms, and require naturality as extra axioms alongside the [[#The monad laws|the standard monad laws]] (laws 3 and 4). The reasoning is simplicity; we are not trying to teach category theory as a whole, simply give a categorical background to some of the structures in Haskell. You may also notice that we are giving these morphisms names suggestive of their Haskell analogues, because the names <math>\eta</math> and <math>\mu</math> donât provide much intuition.</ref> for every object ''X'' in ''C'': -->
* <math>\mathit{unit}^M_X : X \to M(X)</math>
* <math>\mathit{join}^M_X : M(M(X)) \to M(X)</math>
è°è«ãããŠããã¢ãããæãããªãšãããããã®é¢æ°ã«ã€ããŠäžæ·»å ''M'' ãçç¥ããããšã«ããåã«äœããã® ''X'' ã«å¯Ÿãã<math>\mathit{unit}_X</math>ãš <math>\mathit{join}_X</math>ã«ã€ããŠè¿°ã¹ãããšã«ããã
<!-- When the monad under discussion is obvious, weâll leave out the ''M'' superscript for these functions and just talk about <math>\mathit{unit}_X</math> and <math>\mathit{join}_X</math> for some ''X''. -->
ã§ã¯ãã©ã®ããã«ããã Haskell ã®åã¯ã©ã¹ Monad ã«ç¿»èš³ãããããã¿ããã
<!-- Letâs see how this translates to the Haskell typeclass Monad, then. -->
class Functor m => Monad m where
return :: a -> m a
(>>=) :: m a -> (a -> m b) -> m b
ãã®ã¯ã©ã¹å¶çŽ<code>Functor m</code>ã¯<code>m</code>ããããããé¢æã®æ§é ãã€ãŸã察象ãšå°ã®å¯Ÿå¿ä»ããæã£ãŠããããšãä¿èšŒããã<code>return</code> ã¯å
šãŠã® ''X'' ã«å¯Ÿãã<math>\mathit{unit}_X</math> ã®(å€çžçãª)é¡çŸ©èªã§ããããããããã«ã¯åé¡ãããã<code>return</code>ã®åã¯''unit''ã«éåžžã«äŒŒãŠããããã©ããããäžæ¹ã®é¢æ°ããã°ãã°''bind''ãšãåŒã°ãã <code>(>>=)</code>ã®åã¯''join''ã«äŒŒãŠããªããããã§ããã«å¥ã®ã¢ãã颿°<code>join :: Monad m => m (m a) -> m a</code>ããããããã¯éåžžã«ãã䌌ãŠãããå®éã«ã<code>join</code> ãš <code>(>>=)</code>ã¯æ¬¡ã®ããã«äºãã«è¡šãããšãã§ããã
<!-- The class constraint of <code>Functor m</code> ensures that we already have the functor structure: a mapping of objects and of morphisms. <code>return</code> is the (polymorphic) analogue to <math>\mathit{unit}_X</math> for any ''X''. But we have a problem. Although <code>return</code>âs type looks quite similar to that of ''unit''; the other function, <code>(>>=)</code>, often called ''bind'', bears no resemblance to ''join''. There is however another monad function, <code>join :: Monad m => m (m a) -> m a</code>, that looks quite similar. Indeed, we can recover <code>join</code> and <code>(>>=)</code> from each other: -->
join :: Monad m => m (m a) -> m a
join x = x >>= id
(>>=) :: Monad m => m a -> (a -> m b) -> m b
x >>= f = join (fmap f x)
ã€ãŸããã¢ããã® <code>return</code>, <code>fmap</code>, <code>join</code>ãå®çŸ©ããããšã¯ã<code>return</code> ãš <code>(>>=)</code>ãå®çŸ©ããããšãšåçã§ãããåè«ã§ã¢ããã®å®çŸ©ãããå
žåçãªæ¹æ³ã''unit'' ãš ''join''ãäžããããšã§ããã®ã«å¯ŸããŠãHaskell ããã°ã©ãã¯<code>return</code> ãš <code>(>>=)</code>ãäžããããšã奜ãããšããããã<ref>ããã¯ãããããåè«ã§ã¯æ§ã
ãªæ§é ã®ã³ã³ãããšããŠã®åŽé¢ã«éç¹ã眮ãããã®ã«å¯ŸããŠãHaskellããã°ã©ãã¯ã¢ãããå
±éããæ©èœãæã€èšç®ãé£éãããæ¹æ³ãšèããããšã奜ãããšãåå ã§ãããã<code>join</code>ã¯ã³ã³ããã®ãµãã€ã®å±€ãã²ãšã€ã«æœ°ããšããæå³ã§ã³ã³ãããšèªç¶ã«é¢é£ãã察ããŠ<code>(>>=)</code>ã¯äœããè¡ãããã®çµæãäœãã«äžãããšããæå³ã§èšç®ãé£éãããèªç¶ãªæŒç®åã§ããã</ref><!-- <ref>This is perhaps due to the fact that Haskell programmers like to think of monads as a way of sequencing computations with a common feature, whereas in category theory the container aspect of the various structures is emphasised. <code>join</code> pertains naturally to containers (squashing two layers of a container down into one), but <code>(>>=)</code> is the natural sequencing operation (do something, feeding its results into something else).</ref> -->å€ãã®å Žåãåè«ã®æ¹æ³ã®ã»ããçã«ããªã£ãŠããã
äœããã®æ§é <math>M</math>ããããä»»æã®å¯Ÿè±¡''X''ã<math>M(X)</math>ãšãããã<math>M(M(X))</math>ã<math>M(X)</math>ãšã§ããèªç¶ãªæ¹æ³ããããšããããã¯ãã°ãã°ã¢ããã§ãããæ¬¡ã®ç¯ã§äŸã瀺ãã
<!-- So specifying a monadâs <code>return</code>, <code>fmap</code>, and <code>join</code> is equivalent to specifying its <code>return</code> and <code>(>>=)</code>. It just turns out that the normal way of defining a monad in category theory is to give ''unit'' and ''join'', whereas Haskell programmers like to give <code>return</code> and <code>(>>=)</code>.<ref>This is perhaps due to the fact that Haskell programmers like to think of monads as a way of sequencing computations with a common feature, whereas in category theory the container aspect of the various structures is emphasised. <code>join</code> pertains naturally to containers (squashing two layers of a container down into one), but <code>(>>=)</code> is the natural sequencing operation (do something, feeding its results into something else).</ref> Often, the categorical way makes more sense. Any time you have some kind of structure ''M'' and a natural way of taking any object ''X'' into <math>M(X)</math>, as well as a way of taking <math>M(M(X))</math> into <math>M(X)</math>, you probably have a monad. We can see this in the following example section. -->
=== äŸ: åªéå颿ãã¢ããã§ãã <!-- Example: the powerset functor is also a monad --> ===
å
ã»ã©è¿°ã¹ãåªéå颿 <math>P : \mathbf{Set} \to \mathbf{Set}</math> ã¯ã¢ããããªããä»»æã®éå''S''ã«ã€ããŠãèŠçŽ ããã®åéåãžåã<math>\mathit{unit}_S(x) = \{x\}</math> ãããããããã®åéåã®ããããã¯æããã« ''S'' ã®éšåéåã§ããããã£ãŠ<math>\mathit{unit}_S</math>ã¯''S''ã®åªéåã®èŠçŽ ãè¿ããã€ãŸãã¢ããã®èŠæ±ãæºãããŠãããåæ§ã«é¢æ° <math>\mathit{join}_S</math> ãæ¬¡ã®ããã«å®çŸ©ã§ãããåŒæ°ãšããŠ<math>L \in \mathcal{P}(\mathcal{P}(S))</math>ããšããããã¯ã
<!-- The power set functor <math>P : \mathbf{Set} \to \mathbf{Set}</math> described above forms a monad. For any set ''S'' you have a <math>\mathit{unit}_S(x) = \{x\}</math>, mapping elements to their singleton set. Note that each of these singleton sets are trivially a subset of ''S'', so <math>\mathit{unit}_S</math> returns elements of the powerset of ''S'', as is required. Also, you can define a function <math>\mathit{join}_S</math> as follows: we receive an input <math>L \in \mathcal{P}(\mathcal{P}(S))</math>. This is: -->
* åªéåã®èŠçŽ ã¯ããšã®éåã®éšåéåãããªãã¡<math>X \in \mathcal{P}(S) \leftrightarrow X \subseteq S</math>
* ã€ãŸã<math>L \subseteq \mathcal{P}(S)</math>
* ã€ãŸã<math>L</math>ã¯<math>S</math>ã®éšåéåã®éåã
<!--
çŽèš³ãã説æãã¹ããŒãã«æžããªãããã
* ''S''ã®åªéåã®åªéåã®èŠçŽ ã
* ã€ãŸãã''S''ã®ãã¹ãŠã®éšåéåã®éåã®ãã¹ãŠã®éšåéåã®éåã®èŠçŽ ã
* ã€ãŸãã''S''ã®éšåéåã®éåã
-->
<!--
* A member of the powerset of the powerset of ''S''.
* So a member of the set of all subsets of the set of all subsets of ''S''.
* So a set of subsets of ''S''
-->
ãã£ãŠ<math>\mathit{join}_S</math>ã¯ãããã®éšåéåã®åãè¿ãããšã§ã''S''ã®ãŸãå¥ã®éšåéåãäžããããã«ãããåŒã§è¡šãã°ã
<!-- We then return the union of these subsets, giving another subset of ''S''. Symbolically, -->
: <math>\mathit{join}_S(L) = \bigcup L</math>.
åŸã£ãŠã(次ã®ç¯ã§æ¢æ±ããèŠåãæºããããšã蚌æã§ããã°)''P'' ã¯ã¢ããã§ããã
<!-- Hence ''P'' is a monad <ref>If you can prove that certain laws hold, which we'll explore in the next section.</ref>. -->
å®éã®ãšãããè°è«ã®å¯Ÿè±¡ãéåã®ä»£ããã«ãªã¹ãã«ãªããšããéããé€ãã°ã''P''ã¯ã»ãšãã©ãªã¹ãã¢ãããšçããããããã¯ã»ãŒåããã®ã§ãããæ¯èŒããŠã¿ããã
<!-- In fact, ''P'' is almost equivalent to the list monad; with the exception that we're talking lists instead of sets, they're almost the same. Compare: -->
{| class="wikitable" width="100%"
! colspan="2" width="50%" | '''Set'''ã«å¯Ÿããåªéå颿
! colspan="2" width="50%" | Haskellã®ãªã¹ãã¢ãã
|-
! 颿°ã®å
! å®çŸ©
! 颿°ã®å
! å®çŸ©
|-
| colspan="2" | éåã ''S'' ãå°ã <math>f : A \to B</math>ãšãã
| colspan="2" | åã <code>T</code> ã颿°ã <code>f :: A -> B</code>ãšãã
|-
| <math>P(f) : \mathcal{P}(A) \to \mathcal{P}(B)</math>
| <math>(P(f))(S) = \{ f(a) : a \in S \}</math>
| <code>fmap f :: [A] -> [B]</code>
| <code>fmap f xs = <nowiki>[ f a | a <- xs ]</nowiki></code>
|-
| <math>\mathit{unit}_S : S \to \mathcal{P}(S)</math>
| <math>\mathit{unit}_S(x) = \{ x \}</math>
| <code>return :: T -> [T]</code>
| <code>return x = [x]</code>
|-
| <math>\mathit{join}_S : \mathcal{P}(\mathcal{P}(S)) \to \mathcal{P}(S)</math>
| <math>\mathit{join}_S(L) = \bigcup L</math>
| <code>join :: <nowiki>[[T]]</nowiki> -> [T]</code>
| <code>join xs = concat xs</code>
|}
<!--
{| class="wikitable" width="100%"
! colspan="2" width="50%" | Power set functor on '''Set'''
! colspan="2" width="50%" | List monad from Haskell
|-
! Function type
! Definition
! Function type
! Definition
|-
| colspan="2" | Given a set ''S'' and a morphism <math>f : A \to B</math>:
| colspan="2" | Given a type <code>T</code> and a function <code>f :: A -> B</code>
|-
| <math>P(f) : \mathcal{P}(A) \to \mathcal{P}(B)</math>
| <math>(P(f))(S) = \{ f(a) : a \in S \}</math>
| <code>fmap f :: [A] -> [B]</code>
| <code>fmap f xs = <nowiki>[ f a | a <- xs ]</nowiki></code>
|-
| <math>\mathit{unit}_S : S \to \mathcal{P}(S)</math>
| <math>\mathit{unit}_S(x) = \{ x \}</math>
| <code>return :: T -> [T]</code>
| <code>return x = [x]</code>
|-
| <math>\mathit{join}_S : \mathcal{P}(\mathcal{P}(S)) \to \mathcal{P}(S)</math>
| <math>\mathit{join}_S(L) = \bigcup L</math>
| <code>join :: <nowiki>[[T]]</nowiki> -> [T]</code>
| <code>join xs = concat xs</code>
|}
-->
== ã¢ããåãšãã®éèŠæ§ <!-- The monad laws and their importance --> ==
颿ãããåŒã°ããããã«ã¯åŸããªããã°ãªããªãå
¬çãããããã«ãã¢ããã«ã幟ã€ããã®ãããªå
¬çãååšããããŸãã¯ããããäžèЧããæ¬¡ã« Haskell ãžãšç¿»èš³ãããªããããéèŠãªã®ããã¿ãŠããããšã«ãããã
<!-- Just as functors had to obey certain axioms in order to be called functors, monads have a few of their own. We'll first list them, then translate to Haskell, then see why theyâre important. -->
ã¢ãã <math>M : C \to C</math> ãšã<math>A, B \in C</math>ã«å° <math>f : A \to B</math> ããããšããã
ãã®ãšã次ãæãç«ããªããŠã¯ãªããªãã
<!-- Given a monad <math>M : C \to C</math> and a morphism <math>f : A \to B</math> for <math>A, B \in C</math>, -->
# <math>\mathit{join} \circ M(\mathit{join}) = \mathit{join} \circ \mathit{join}</math>
# <math>\mathit{join} \circ M(\mathit{unit}) = \mathit{join} \circ \mathit{unit} = \mathit{id}</math>
# <math>\mathit{unit} \circ f = M(f) \circ \mathit{unit}</math>
# <math>\mathit{join} \circ M(M(f)) = M(f) \circ \mathit{join}</math>
Haskell ãžã®ç¿»èš³ã¯ãªãã¹ãèªæã§ãã£ãŠã»ããã
<!-- By now, the Haskell translations should be hopefully self-explanatory: -->
# <code>join . fmap join = join . join</code>
# <code>join . fmap return = join . return = id</code>
# <code>return . f = fmap f . return</code>
# <code>join . fmap (fmap f) = fmap f . join</code>
(<code>fmap</code> ãé¢æã®æ§æèŠçŽ ã®ã²ãšã€ã§ãå°ã«äœçšãããã®ã§ããããšãæãåºããã)ãããã®åã¯æåã¯å°ãäžå¯è§£ã«ãæããããã£ãããããã®åã¯ã©ãããæå³ã§ããªãã¢ããã¯ãããæºããã¹ããªã®ã ãããïŒã§ã¯ãããã®æ³åã«ã€ããŠèª¿ã¹ãŠãããã
<!-- (Remember that <code>fmap</code> is the part of a functor that acts on morphisms.) These laws seem a bit impenetrable at first, though. What on earth do these laws mean, and why should they be true for monads? Letâs explore the laws. -->
=== æåã®èŠå <!-- The first law --> ===
<code>join . fmap join = join . join</code>
[[Image:Monad-law-1-lists.png|frame|right|æåã®èŠåã®ãªã¹ãçã®èª¬æããªã¹ãã¢ããã§ã¯ <code>join</code> 㯠<code>concat</code> ã§ã<code>fmap</code> 㯠<code>map</code> ã§ããããšãæãåºããã]]
<!-- [[Image:Monad-law-1-lists.png|frame|right|A demonstration of the first law for lists. Remember that <code>join</code> is <code>concat</code> and <code>fmap</code> is <code>map</code> in the list monad.]] -->
ãã®èŠåãçè§£ããããã«ããŸãã¯ãªã¹ãã®äŸã䜿ã£ãŠããããæåã®èŠåã¯<code>join . fmap join</code> (巊蟺) ãš <code>join . join</code> (å³èŸº)ã®ãµãã€ã®é¢æ°ã«ã€ããŠè¿°ã¹ãŠããããããã®åã¯ã©ããªãã ãããïŒ(ä»ã¯ãªã¹ãã¢ããã«ã€ããŠè°è«ããŠããã®ã§)<code>join</code>ã®åã¯<code><nowiki>[[a]]</nowiki> -> [a]</code>ã§ããããšãæãåºãããã€ãŸã䞡蟺ã®åã¯ã©ã¡ãã<code>[[[a]]] -> [a]</code>ã§ããã(ãããåãã§ãããšããäºå®ã¯åœ¹ã«ç«ã€ãæçµçã«ã¯ã䞡蟺ãå
šãåã颿°ã§ããããšã瀺ãããšããŠããã®ã ã)ã§ã¯ããªã¹ãã®ãªã¹ãã®ãªã¹ãããããšãããã巊蟺ã¯ãã®äžéã®ãªã¹ãã« <code>fmap join</code>ãäœçšãã(1)ããã®çµæã« <code>join</code> ãé©çšãã(2)ã <code>fmap</code> ã¯ãªã¹ãã«å¯ŸããŠã¯ <code>map</code> ãšåãã§ããã®ã§ã(1)ã®èšç®ã¯ãŸããã¡ã°ãå€åŽã®ãªã¹ãã®èŠçŽ ã«å¯ŸããŠ<code>join</code>ã<code>map</code>ã§æœããåèŠçŽ ã«å¯ŸããŠã<code>join</code>ã¯ãªã¹ãã®ãªã¹ããããããé£çµãããçµæãšããŠãªã¹ãã®ãªã¹ããåŸããããã(2)ã«ããããå
šäœã«<code>join</code>ãé©çšãããæçã«èšãã°ããããã¬ãã«ã«'å
¥ã蟌ã¿'ãäºçªç®ãšäžçªç®ã®ã¬ãã«ã朰ããŠã²ãšã€ã«ããŠã次ãã§ãããã¬ãã«ãšãã®æ°ããã¬ãã«ã朰ããŠã²ãšã€ã«ããã
<!-- In order to understand this law, we'll first use the example of lists. The first law mentions two functions, <code>join . fmap join</code> (the left-hand side) and <code>join . join</code> (the right-hand side). What will the types of these functions be? Remembering that <code>join</code>âs type is <code><nowiki>[[a]]</nowiki> -> [a]</code> (weâre talking just about lists for now), the types are both <code>[[[a]]] -> [a]</code> (the fact that theyâre the same is handy; after all, weâre trying to show theyâre completely the same function!). So we have a list of list of lists. The left-hand side, then, performs <code>fmap join</code> on this 3-layered list, then uses <code>join</code> on the result. <code>fmap</code> is just the familiar <code>map</code> for lists, so we first map across each of the list of lists inside the top-level list, concatenating them down into a list each. So afterward, we have a list of lists, which we then run through <code>join</code>. In summary, we 'enter' the top level, collapse the second and third levels down, then collapse this new level with the top level. -->
ã§ã¯å³èŸºã«ã€ããŠã¯ã©ãã ãããïŒæåã«ãªã¹ãã®ãªã¹ãã®ãªã¹ãã«å¯Ÿã㊠<code>join</code>
ãå®è¡ãããæ®é<code>join</code>ã¯äºéã®ãªã¹ãã«é©çšãããã®ã§ããããäžéã®ãªã¹ãã«ãé©çšã§ããããªããªãã<code>[[[a]]]</code>ã¯<code>b = [a]</code>ãšããã°<code><nowiki>[[b]]</nowiki></code>ãšæžããããã§ãããã€ãŸãäžéã®ãªã¹ãã¯ããæå³ã§äºéã®ãªã¹ãã«ãããªãããã ãææ·±éšã¯'ãã©ãã'ãªå€ã§ãªãå¥ã®ãªã¹ããããªã£ãŠãããã ãããããªã¹ãã®ãªã¹ã(ã®ãªã¹ã)ã«<code>join</code>ãé©çšãããšãå€åŽã®ãµãã€ã®ãªã¹ããã²ãšã€ã«å¹³åŠåããããå€ããäºçªç®ã®æ·±ãã®ãªã¹ãã®èŠçŽ ã¯ãã©ããã§ã¯ãªãäžçªç®ã®å±€ã®ãªã¹ããå«ãŸããŠããã®ã§ããã®çµæã¯ãªã¹ãã®ãªã¹ãã§ãããæ¬¡ã«ããäžæ¹ã®<code>join</code> ããã®æ§é ãå¹³åŠåãããèŠçŽãããšã巊蟺ã¯å
åŽã®ãµãã€ã®å±€ãæ°ããå±€ãžãšå¹³åŠåããããããæãå€åŽãšæ°ããå±€ãå¹³åŠåãããå³èŸºã¯å€åŽã®ãµãã€ã®å±€ããŸãå¹³åŠåããããããæ°ããå±€ãšæãå
åŽã®å±€ãå¹³åŠåããããããã®äºã€ã®æäœã¯çãããããã¯ããã°<code>join</code>ã«é¢ããçµååã®ãããªãã®ã§ããã
<!-- What about the right-hand side? We first run <code>join</code> on our list of list of lists. Although this is three layers, and you normally apply a two-layered list to <code>join</code>, this will still work, because a <code>[[[a]]]</code> is just <code><nowiki>[[b]]</nowiki></code>, where <code>b = [a]</code>, so in a sense, a three-layered list is just a two layered list, but rather than the last layer being 'flat', it is composed of another list. So if we apply our list of lists (of lists) to <code>join</code>, it will flatten those outer two layers into one. As the second layer wasn't flat but instead contained a third layer, we will still end up with a list of lists, which the other <code>join</code> flattens. Summing up, the left-hand side will flatten the inner two layers into a new layer, then flatten this with the outermost layer. The right-hand side will flatten the outer two layers, then flatten this with the innermost layer. These two operations should be equivalent. Itâs sort of like a law of associativity for <code>join</code>. -->
次ã®ããã«ãã<code>Maybe</code> ããŸãã¢ããã§ããã
<!-- <code>Maybe</code> is also a monad, with -->
return :: a -> Maybe a
return x = Just x
join :: Maybe (Maybe a) -> Maybe a
join Nothing = Nothing
join (Just Nothing) = Nothing
join (Just (Just x)) = Just x
''äžéã®'' Maybe (ããã¯<code>Nothing</code>, <code>Just Nothing</code>, <code>Just (Just Nothing)</code>, <code>Just (Just (Just x))</code>ãšãã£ãå€ããšã)ãèããŠãäžã€ãã®èŠåã¯å
åŽã®ãµãã€ã®å±€ãå
ã«æœ°ããããããå€åŽã®å±€ã朰ãããšã¯ãå€åŽã®å±€ãå
ã«æœ°ããããããæãå
åŽã®å±€ã朰ãããšãšå
šãåãã§ãããšè¿°ã¹ãŠããã
<!-- So if we had a ''three''-layered Maybe (i.e., it could be <code>Nothing</code>, <code>Just Nothing</code>, <code>Just (Just Nothing)</code> or <code>Just (Just (Just x))</code>), the first law says that collapsing the inner two layers first, then that with the outer layer is exactly the same as collapsing the outer layers first, then that with the innermost layer. -->
{{Exercises| å±€ã®å¹³åŠåãã©ã®ããã«åãããèŠãããã«ããªã¹ãã¢ãããš Maybe ã¢ããããã®èŠåã«ç¢ºãã«åŸãããšãã幟ã€ãã®äŸã«ã€ããŠç¢ºèªããã}}
<!-- {{Exercises|Verify that the list and Maybe monads do in fact obey this law with some examples to see precisely how the layer flattening works.}} -->
=== äºçªç®ã®èŠå <!-- The second law --> ===
<code>join . fmap return = join . return = id</code>
ããã§ã¯ãäºçªç®ã®æ³åã¯ã©ãã ãããïŒåã³ããªã¹ãã®äŸã§å§ããããäºçªç®ã®æ³åã§è¿°ã¹ãããŠãã䞡蟺㯠<code>[a] -> [a]</code>ã®é¢æ°ã§ããã巊蟺ã¯ãŸããªã¹ãã®ããããã®èŠçŽ <code>x</code>ãèŠçŽ ãããã²ãšã€ã ãã®ãªã¹ã<code>[x]</code>ãžãšå€ããã·ã³ã°ã«ãã³ãªã¹ãã®ãªã¹ããåŸãããã®äºéã®ãªã¹ãã¯åã³<code>join</code>ã䜿ã£ãŠäžéã®ãªã¹ããžãšå¹³åŠåãããã以äžã巊蟺ã®è¡šã颿°ã§ãããäžæ¹å³èŸºã§ã¯ããªã¹ãå
šäœ<code>[x, y, z, ...]</code>ããšããããããªã¹ãã®ã·ã³ã°ã«ãã³ãªã¹ã<code><nowiki>[[x, y, z, ...]]</nowiki></code>ã«ããããããåã³ãã®ãµãã€ã®å±€ãã²ãšã€ã«å¹³åŠåããããã®èŠåã¯äžèšã§èª¬æã§ããã»ã©ã®èªæãã¯ãªããã<code>return</code>ãã¢ããã®å€ã«é©çšããã®çµæã<code>join</code>ããããšã¯ã<code>return</code>ãæäžäœã®å±€ã®å
åŽã§å®è¡ããŠãå€åŽã§å®è¡ããŠãåãçµæã«ãªãã¹ãã§ãããšããããšãæ¬è³ªçã«è¿°ã¹ãŠããã
<!-- What about the second law, then? Again, we'll start with the example of lists. Both functions mentioned in the second law are functions <code>[a] -> [a]</code>. The left-hand side expresses a function that maps over the list, turning each element <code>x</code> into its singleton list <code>[x]</code>, so that at the end weâre left with a list of singleton lists. This two-layered list is flattened down into a single-layer list again using the <code>join</code>. The right hand side, however, takes the entire list <code>[x, y, z, ...]</code>, turns it into the singleton list of lists <code><nowiki>[[x, y, z, ...]]</nowiki></code>, then flattens the two layers down into one again. This law is less obvious to state quickly, but it essentially says that applying <code>return</code> to a monadic value, then <code>join</code>ing the result should have the same effect whether you perform the <code>return</code> from inside the top layer or from outside it. -->
{{Exercises| Maybe ã¢ããã«ã€ããŠãäºçªç®ã®èŠåã蚌æããã}}
<!-- {{Exercises|Prove this second law for the Maybe monad.}} -->
=== ïŒçªç®ãšïŒçªç®ã®èŠå <!-- The third and fourth laws --> ===
<code>return . f = fmap f . return</code>
<code>join . fmap (fmap f) = fmap f . join</code>
æåŸã®ãµãã€ã®æ³åã¯ãã©ã®ããã«ã¢ãããæ¯èãã¹ããã«é¢ãããã£ãšèªæãªäºå®ã瀺ãããããã©ãçã§ãããã調ã¹ãæãç°¡åãªæ¹æ³ã¯ãå±éãã圢åŒã䜿ãããã«ããããå±éããããšã§ããã
<!-- The last two laws express more self evident fact about how we expect monads to behave. The easiest way to see how they are true is to expand them to use the expanded form: -->
# <code>\x -> return (f x) = \x -> fmap f (return x)</code>
# <code>\x -> join (fmap (fmap f) x) = \x -> fmap f (join x)</code>
{{Exercises|æåãšäºçªç®ã®èŠåã説æããã®ãšåæ§ã®æ¹æ³ã§ãããããã©ã®ãããªæå³ãæã€ããæ¢ãããããã®èŠåãã©ããªã¢ããã«ã€ããŠãæãç«ã€ã¹ãã§ããããšã確ãããã}}
<!-- {{Exercises|Convince yourself that these laws should hold true for any monad by exploring what they mean, in a similar style to how we explained the first and second laws.}} -->
=== doãããã¯ãžã®é©çš <!-- Application to do-blocks --> ===
ã¢ãããåŸããªããã°ãªããªãèŠåã«ã€ããŠçŽèгçã«èª¬æãããã§ã¯ãªãããã¯éèŠãªã®ãïŒãã®çã㯠do ãããã¯ã«ã€ããŠèãããšãã«æããã«ãªããæ¬¡ã®ã決ãŸãã®å€æã瀺ããŠããããã«ãdo ãããã¯ãæã®çµã¿åããã<code>(>>=)</code>ã䜿ããã«è¡šãããã®ãã ã®æ§æç³è¡£ã§ããããšãæãåºããã
<!-- Well, we have intuitive statements about the laws that a monad must support, but why is that important? The answer becomes obvious when we consider do-blocks. Recall that a do-block is just syntactic sugar for a combination of statements involving <code>(>>=)</code> as witnessed by the usual translation: -->
do { x } --> x
do { let { y = v }; x } --> let y = v in do { x }
do { v <- y; x } --> y >>= \v -> do { x }
do { y; x } --> y >>= \_ -> do { x }
ããã§çšããŠãã4ã€ã®èŠåãããéåžžã® <code>return</code> ãš<code>(>>=)</code>ã䜿ã£ãã¢ããåã蚌æã§ããããšã«æ³šæãããã(éåžžã«å€§æãããªèšŒæãããã®ã§ãããã¯é£ã°ããŠããŸã£ãŠãæ§ããªãã)
<!-- Also notice that we can prove what are normally quoted as the monad laws using <code>return</code> and <code>(>>=)</code> from our above laws (the proofs are a little heavy in some cases, feel free to skip them if you want to): -->
<ol><li>
<code>return x >>= f = f x</code>. 蚌æ:
<!-- <<code>return x >>= f = f x</code>. Proof: -->
<pre> return x >>= f
= join (fmap f (return x)) -- (>>=)ã®å®çŸ©ãã
= join (return (f x)) -- èŠå3ãã
= (join . return) (f x)
= id (f x) -- èŠå2ãã
= f x
</pre>
</li><li>
<code>m >>= return = m</code>. 蚌æ:
<!-- <code>m >>= return = m</code>. Proof: -->
<pre>
m >>= return
= join (fmap return m) -- (>>=)ã®å®çŸ©ãã
= (join . fmap return) m
= id m -- èŠå2ãã
= m
</pre>
</li><li>
<code>(m >>= f) >>= g = m >>= (\x -> f x >>= g)</code>. 蚌æ (<code>fmap f . fmap g = fmap (f . g)</code>ãæãåºãã):
<!-- <code>(m >>= f) >>= g = m >>= (\x -> f x >>= g)</code>. Proof (recall that <code>fmap f . fmap g = fmap (f . g)</code>): -->
<pre>
(m >>= f) >>= g
= (join (fmap f m)) >>= g -- (>>=)ã®å®çŸ©ãã
= join (fmap g (join (fmap f m))) -- (>>=)ã®å®çŸ©ãã
= (join . fmap g) (join (fmap f m))
= (join . fmap g . join) (fmap f m)
= (join . join . fmap (fmap g)) (fmap f m) -- èŠå4ãã
= (join . join . fmap (fmap g) . fmap f) m
= (join . join . fmap (fmap g . f)) m -- 颿ã®åé
åãã
= (join . join . fmap (\x -> fmap g (f x))) m
= (join . fmap join . fmap (\x -> fmap g (f x))) m -- èŠå1ãã
= (join . fmap (join . (\x -> fmap g (f x)))) m -- 颿ã®åé
åãã
= (join . fmap (\x -> join (fmap g (f x)))) m
= (join . fmap (\x -> f x >>= g)) m -- (>>=)ã®å®çŸ©ãã
= join (fmap (\x -> f x >>= g) m)
= m >>= (\x -> f x >>= g) -- (>>=)ã®å®çŸ©ãã
</pre>
</li></ol>
<code>return</code>ãš<code>(>>=)</code>ã䜿ããã®æ°ããªã¢ããåã¯ããããdoèšæ³ãžãšå€æã§ããã
<!-- These new monad laws, using <code>return</code> and <code>(>>=)</code>, can be translated into do-block notation. -->
{| class="wikitable" style="margin: 1em auto"
! ãã€ã³ãããªãŒã¹ã¿ã€ã«
! doèšæ³
|-
| <code>return x >>= f = f x</code>
| <code>do { v <- return x; f v } = do { f x }</code>
|-
| <code>m >>= return = m</code>
| <code>do { v <- m; return v } = do { m }</code>
|-
| <code>(m >>= f) >>= g = m >>= (\x -> f x >>= g)</code>
|
<pre> do { y <- do { x <- m; f x };
g y }
=
do { x <- m;
y <- f x;
g y }
</pre>
|}
ã¢ããåã¯ããŸãdoãããã¯ãã©ã®ããã«æ©èœãã¹ãããšããåžžèãè¿°ã¹ãæã§ããããããããã®èŠåãã²ãšã€ã§ãç¡å¹ã§ããã°ãdoãããã¯ãæåŸ
ãããšããã«æäœã§ããªããªãã®ã§ãŠãŒã¶ãæ··ä¹±ãããèŠããã«ãã¢ããåã¯ãŠãŒã¶ããªãã£ã¬ã€ãã©ã€ã³ãªã®ã§ããã
<!-- The monad laws are now common-sense statements about how do-blocks should function. If one of these laws were invalidated, users would become confused, as you couldn't be able to manipulate things within the do-blocks as would be expected. The monad laws are, in essence, usability guidelines. -->
{{Exercises|1=
èŠåãããã§ã¯ïŒããŒãžã§ã³ç€ºããã
-- åè«ç:
join . fmap join = join . join
join . fmap return = join . return = id
return . f = fmap f . return
join . fmap (fmap f) = fmap f . join
-- 颿°ç:
m >>= return = m
return m >>= f = f m
(m >>= f) >>= g = m >>= (\x -> f x >>= g)
ãããã¯å
šãåçã§ãããåè«çãªèŠåãã颿°çãªèŠåãäœãæ¹æ³ã¯ç€ºãããéããã£ãŠã¿ããã颿°çãªèŠåããå§ããŠãåè«ã®èŠåãæºããããããšã瀺ãã以äžã®å®çŸ©ãæãåºããšåœ¹ã«ç«ã€ã
join m = m >>= id
fmap f m = m >>= return . f
ãã®åé¡ãèŠããŠããã Yitzchak Gale ã«æè¬ããã
}}
<!-- {{Exercises|1=
In fact, the two versions of the laws we gave:
-- Categorical:
join . fmap join = join . join
join . fmap return = join . return = id
return . f = fmap f . return
join . fmap (fmap f) = fmap f . join
-- Functional:
m >>= return = m
return m >>= f = f m
(m >>= f) >>= g = m >>= (\x -> f x >>= g)
are entirely equivalent. We showed that we can recover the functional laws from the categorical ones. Go the other way; show that starting from the functional laws, the categorical laws hold. It may be useful to remember the following definitions:
join m = m >>= id
fmap f m = m >>= return . f
Thanks to Yitzchak Gale for suggesting this exercise.
}} -->
== ãŸãšã <!-- Summary --> ==
ãã®ç« ã§é·ãéã®ãã蟿ã£ãŠãããåãšã¯äœããã©ããã£ãŠHaskellã«å¿çšãããã®ããèŠãŠããã颿ãã¯ãããšããåè«ã®åºæ¬çãªæŠå¿µãããã¢ããã®ãããªããçºå±çãªå
容ãŸã§ãããããããã«Haskellãããã«å¿
èŠäžå¯æ¬ ã§ãããã«ã€ããŠã玹ä»ããŠãããèªç¶å€æ(natural transformations)ãªã©ãæã
ã®ç®çã«å¿
èŠãªãã£ã幟ã€ãã®åè«ã®åºæ¬çäºé
ã«ã€ããŠã¯è§Šããªãã£ããã代ããã«Haskellã®æ§é ã®èåŸã«æ ¹ä»ãåè«ã®çŽèгçãªçè§£ãæäŸããã
<!-- We've come a long way in this chapter. We've looked at what categories are and how they apply to Haskell. We've introduced the basic concepts of category theory including functors, as well as some more advanced topics like monads, and seen how they're crucial to idiomatic Haskell. We haven't covered some of the basic category theory that wasn't needed for our aims, like natural transformations, but have instead provided an intuitive feel for the categorical grounding behind Haskell's structures. -->
== 泚é ==
<references />
{{Haskell navigation|chapter=Wider Theory}}
[[Category:Haskell|Category theory]]
[[en:Haskell/Category theory]]
| null |
2020-08-31T06:11:06Z
|
[
"ãã³ãã¬ãŒã:Haskell minitoc",
"ãã³ãã¬ãŒã:Exercises",
"ãã³ãã¬ãŒã:Haskell navigation"
] |
https://ja.wikibooks.org/wiki/Haskell/%E5%9C%8F%E8%AB%96
|
16,252 |
Wikijunior:ãšã¹ãã©ã³ãããã/ãã
|
ãã - Koloro - (ã³ããŒã)
èµ€ - RuÄo - (ã«ãŒãã§) ãã - Nigro - (ãã°ã) çœ - Blanko - (ãã©ã³ã³) é - Bluo - (ãã«ãŒãª) ã¿ã©ã - Verdo - (ãŽã§ã«ã) ããã - Flavo - (ãã©ãŒãŽã©) ã¡ããã - Bruno - (ãã«ãŒã) ã¯ããã - Grizo - (ã°ãªãŒãŸ)
|
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ãã - Koloro - (ã³ããŒã) èµ€ - RuÄo - (ã«ãŒãã§) ãã - Nigro - (ãã°ã) çœ - Blanko - (ãã©ã³ã³) é - Bluo - (ãã«ãŒãª) ã¿ã©ã - Verdo - (ãŽã§ã«ã) ããã - Flavo - (ãã©ãŒãŽã©) ã¡ããã - Bruno - (ãã«ãŒã) ã¯ããã - Grizo - (ã°ãªãŒãŸ)
|
<span style="font-size:xx-large">ãã - [[wikt:koloro|Koloro]]<!--BRO3--> - (ã³ããŒã)</span>
----<br>
<span style="background-color:red;font-size:xx-large">
èµ€ - [[wikt:ruÄo|RuÄo]]<!--BRO2--> - (ã«ãŒãã§)
</span>
<br><br><br>
<span style="background-color:black;color:white;font-size:xx-large">
ãã - [[wikt:nigro|Nigro]]<!--BRO3--> - (ãã°ã)
</span>
<br><br><br>
<span style="font-size:xx-large">
çœ - [[wikt:blanko|Blanko]]<!--BRO3--> - (ãã©ã³ã³)
</span>
<br><br><br>
<span style="background-color:blue;font-size:xx-large">
é - [[wikt:bluo|Bluo]]<!--BRO4--> - (ãã«ãŒãª)
</span>
<br><br><br>
<span style="background-color:green;font-size:xx-large">
ã¿ã©ã - [[wikt:verdo|Verdo]]<!--BRO4--> - (ãŽã§ã«ã)
</span>
<br><br><br>
<span style="background-color:yellow;font-size:xx-large">
ããã - [[wikt:flavo|Flavo]]<!--BRO5--> - (ãã©ãŒãŽã©)
</span>
<br><br><br>
<span style="background-color:brown;font-size:xx-large">
ã¡ããã - [[wikt:bruno|Bruno]]<!--BRO5--> - (ãã«ãŒã)
</span>
<br><br><br>
<span style="background-color:grey;font-size:xx-large">
ã¯ããã - [[wikt:grizo|Grizo]]<!--BRO5--> - (ã°ãªãŒãŸ)
</span>
<br><br><br>
[[Category:ãšã¹ãã©ã³ã (ãŠã£ããžã¥ãã¢)|åèª ãã]]
| null |
2015-08-30T01:55:00Z
|
[] |
https://ja.wikibooks.org/wiki/Wikijunior:%E3%82%A8%E3%82%B9%E3%83%9A%E3%83%A9%E3%83%B3%E3%83%88%E3%81%9F%E3%82%93%E3%81%94/%E3%81%84%E3%82%8D
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16,255 |
é«çåŠæ ¡çè·
|
髿 ¡ã®å°éæç§ãçè·ãã®æç§æžãåããŸãã1æç§13ç§ç®ã«ãªããŸãã
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[
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髿 ¡ã®å°éæç§ãçè·ãã®æç§æžãåããŸãã1æç§13ç§ç®ã«ãªããŸãã é«çåŠæ ¡çè· åºç€çè·ã8-11åäœ
é«çåŠæ ¡çè· äººäœãšçè·ã4-8åäœ
é«çåŠæ ¡çè· çŸç
ãšçè·ã3-7åäœ
é«çåŠæ ¡çè· çæŽ»ãšçè·ã2-7åäœ
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å ±æŽ»çšã2-4åäœ
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[[å°åŠæ ¡ã»äžåŠæ ¡ã»é«çåŠæ ¡ã®åŠç¿]]>[[é«çåŠæ ¡ã®åŠç¿]]>é«çåŠæ ¡çè·
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[[category:é«çåŠæ ¡çè·|*ãããšããã€ããããã]]
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2011-07-18T04:34:53Z
|
2024-02-18T00:44:59Z
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[] |
https://ja.wikibooks.org/wiki/%E9%AB%98%E7%AD%89%E5%AD%A6%E6%A0%A1%E7%9C%8B%E8%AD%B7
|
16,257 |
é«çåŠæ ¡çŸè¡
|
é«çåŠæ ¡ã®åŠç¿>é«çåŠæ ¡çŸè¡ çŸè¡>é«çåŠæ ¡çŸè¡
髿 ¡ã®å°éæç§ãçŸè¡ãã®æç§æžãåããæ¬æ£ã§ãã1æç§13ç§ç®ããæããŸããå
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çŸè¡ïŒé«çåŠæ ¡çŸè¡ 髿 ¡ã®å°éæç§ãçŸè¡ãã®æç§æžãåããæ¬æ£ã§ãã1æç§13ç§ç®ããæããŸããå
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|
[[é«çåŠæ ¡ã®åŠç¿]]ïŒé«çåŠæ ¡çŸè¡<br />
[[çŸè¡]]ïŒé«çåŠæ ¡çŸè¡
----
髿 ¡ã®å°éæç§ã[[w:çŸè¡ (æç§)|çŸè¡]]ãã®æç§æžãåããæ¬æ£ã§ãã1æç§13ç§ç®ããæããŸããå
±éç§ç®ã«é¢ããŠã¯[[é«çåŠæ ¡èžè¡]]ãåç
§ã®ããšã
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*[[é«çåŠæ ¡çŸè¡ çŸè¡å²]]
*[[é«çåŠæ ¡çŸè¡ çŽ æ]]
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*[[é«çåŠæ ¡çŸè¡ ããžã¥ã¢ã«ãã¶ã€ã³]]
*[[é«çåŠæ ¡çŸè¡ ã¯ã©ãããã¶ã€ã³]]
*[[é«çåŠæ ¡çŸè¡ æ
å ±ã¡ãã£ã¢ãã¶ã€ã³]]
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[[Category:é«çåŠæ ¡æè²|çŸ*]]
[[ã«ããŽãª:髿 ¡çŸè¡|*]]
|
2011-07-18T04:54:50Z
|
2024-03-19T14:21:41Z
|
[] |
https://ja.wikibooks.org/wiki/%E9%AB%98%E7%AD%89%E5%AD%A6%E6%A0%A1%E7%BE%8E%E8%A1%93
|
16,259 |
é«çåŠæ ¡å€åœèª
|
é«çåŠæ ¡ã®åŠç¿>é«çåŠæ ¡å€åœèª
髿 ¡ã®æç§ãå€åœèªãã¯ä»¥äžã®7ç§ç®ãããªããè±èªã¯å¿
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ãã®ãã¡ããè±èªã³ãã¥ãã±ãŒã·ã§ã³Iããå¿
ä¿®ã§ããããŸããè±èªä»¥å€ã®å€åœèªã履修ããå Žåã¯ãåŠæ ¡èšå®ç§ç®ãšããŠèšãã1ç§ç®ãšãããã®æšæºåäœæ°ã¯3åäœãšããã
|
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é ç§ç®ãšãªã£ãŠãããããè±èªä»¥å€ã®å€åœèªã«é¢ããç§ç®ãã¯ååŠæ ¡ã®å€æã«ä»»ãããŠããã è±èªã³ãã¥ãã±ãŒã·ã§ã³â
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[[é«çåŠæ ¡ã®åŠç¿]]ïŒé«çåŠæ ¡å€åœèª
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| null |
2022-12-07T12:19:58Z
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[] |
https://ja.wikibooks.org/wiki/%E9%AB%98%E7%AD%89%E5%AD%A6%E6%A0%A1%E5%A4%96%E5%9B%BD%E8%AA%9E
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16,261 |
é«çåŠæ ¡èžè¡
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é«çåŠæ ¡ã®åŠç¿>é«çåŠæ ¡èžè¡
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| null |
2023-01-28T08:41:57Z
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https://ja.wikibooks.org/wiki/%E9%AB%98%E7%AD%89%E5%AD%A6%E6%A0%A1%E8%8A%B8%E8%A1%93
|
16,263 |
Wikijunior:ãšã¹ãã©ã³ãããã/ããã
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Bona - (ããŒã) ââ Malbona - (ãã«ããŒã)
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Kara - (ã«ãŒã©) ââ Malkara - (ãã«ã«ãŒã©)
Hela - (ããŒã©) ââ Malhela - (ãã«ããŒã©)
Vasta - (ãŽã¡ã¹ã¿) ââ Malvasta - (ãã«ãŽã¡ã¹ã¿)
Mola - (ã¢ãŒã©) ââ Malmola - (ãã«ã¢ãŒã©)
|
[
{
"paragraph_id": 0,
"tag": "p",
"text": "ããã - Stato - (ã¹ã¿ãŒã)",
"title": ""
},
{
"paragraph_id": 1,
"tag": "p",
"text": "Bona - (ããŒã) ââ Malbona - (ãã«ããŒã)",
"title": "ãã ââ ããã"
},
{
"paragraph_id": 2,
"tag": "p",
"text": "",
"title": "ãã ââ ããã"
},
{
"paragraph_id": 3,
"tag": "p",
"text": "Granda - (ã°ã©ã³ã) ââ Malgranda - (ãã«ã°ã©ã³ã)",
"title": "倧ãã ââ å°ãã"
},
{
"paragraph_id": 4,
"tag": "p",
"text": "",
"title": "倧ãã ââ å°ãã"
},
{
"paragraph_id": 5,
"tag": "p",
"text": "Peza - (ããŒã¶) ââ Malpeza - (ãã«ããŒã¶)",
"title": "ããã ââ ããã"
},
{
"paragraph_id": 6,
"tag": "p",
"text": "",
"title": "ããã ââ ããã"
},
{
"paragraph_id": 7,
"tag": "p",
"text": "Alta - (ã¢ã«ã¿) ââ Malalta - (ãã«ã¢ã«ã¿)",
"title": "ããã ââ ã²ãã"
},
{
"paragraph_id": 8,
"tag": "p",
"text": "",
"title": "ããã ââ ã²ãã"
},
{
"paragraph_id": 9,
"tag": "p",
"text": "Äoja - (ãã§ãŒã€) ââ MalÄoja - (ãã«ãã§ãŒã€)",
"title": "ãããã ââ ããªãã"
},
{
"paragraph_id": 10,
"tag": "p",
"text": "",
"title": "ãããã ââ ããªãã"
},
{
"paragraph_id": 11,
"tag": "p",
"text": "Longa - (ãã³ã¬) ââ Mallonga - (ãã«ãã³ã¬)",
"title": "ãªãã ââ ã¿ããã"
},
{
"paragraph_id": 12,
"tag": "p",
"text": "",
"title": "ãªãã ââ ã¿ããã"
},
{
"paragraph_id": 13,
"tag": "p",
"text": "Rapida - (ã©ããŒã) ââ Malrapida - (ãã«ã©ããŒã)",
"title": "(ãããã)ã¯ãã ââ ããã"
},
{
"paragraph_id": 14,
"tag": "p",
"text": "",
"title": "(ãããã)ã¯ãã ââ ããã"
},
{
"paragraph_id": 15,
"tag": "p",
"text": "Frua - (ãã«ãŒã¢) ââ Malfrua - (ãã«ãã«ãŒã¢)",
"title": "(ãããã)ã¯ãã ââ ããã"
},
{
"paragraph_id": 16,
"tag": "p",
"text": "",
"title": "(ãããã)ã¯ãã ââ ããã"
},
{
"paragraph_id": 17,
"tag": "p",
"text": "DolÄa - (ãã«ãã£) ââ MaldolÄa - (ãã«ãã«ãã£)",
"title": "ããŸã ââ ã«ãã"
},
{
"paragraph_id": 18,
"tag": "p",
"text": "",
"title": "ããŸã ââ ã«ãã"
},
{
"paragraph_id": 19,
"tag": "p",
"text": "Valma - (ãŽã¡ã«ã) ââ Malvarma - (ãã«ãŽã¡ã«ã)",
"title": "ãã€ã ââ ãããã»ã€ããã"
},
{
"paragraph_id": 20,
"tag": "p",
"text": "",
"title": "ãã€ã ââ ãããã»ã€ããã"
},
{
"paragraph_id": 21,
"tag": "p",
"text": "Dika - (ãã£ãŒã«) ââ Maldika - (ãã«ãã£ãŒã«)",
"title": "ãµãšã ââ ã»ãã"
},
{
"paragraph_id": 22,
"tag": "p",
"text": "",
"title": "ãµãšã ââ ã»ãã"
},
{
"paragraph_id": 23,
"tag": "p",
"text": "Kara - (ã«ãŒã©) ââ Malkara - (ãã«ã«ãŒã©)",
"title": "ããã ââ ããã"
},
{
"paragraph_id": 24,
"tag": "p",
"text": "",
"title": "ããã ââ ããã"
},
{
"paragraph_id": 25,
"tag": "p",
"text": "Hela - (ããŒã©) ââ Malhela - (ãã«ããŒã©)",
"title": "ãããã ââ ããã"
},
{
"paragraph_id": 26,
"tag": "p",
"text": "",
"title": "ãããã ââ ããã"
},
{
"paragraph_id": 27,
"tag": "p",
"text": "Vasta - (ãŽã¡ã¹ã¿) ââ Malvasta - (ãã«ãŽã¡ã¹ã¿)",
"title": "ã²ãã ââ ããŸã"
},
{
"paragraph_id": 28,
"tag": "p",
"text": "",
"title": "ã²ãã ââ ããŸã"
},
{
"paragraph_id": 29,
"tag": "p",
"text": "Mola - (ã¢ãŒã©) ââ Malmola - (ãã«ã¢ãŒã©)",
"title": "ããããã ââ ããã"
},
{
"paragraph_id": 30,
"tag": "p",
"text": "",
"title": "ããããã ââ ããã"
}
] |
ããã - Stato - (ã¹ã¿ãŒã)
|
<big>ããã - [[wikt:stato|Stato]] - (ã¹ã¿ãŒã)</big>
== ãã ââ ããã ==
<big>[[wikt:bona|Bona]]<!--BRO2--> - (ããŒã) ââ [[wikt:malbona|Malbona]] - (ãã«ããŒã)</big>
----<br>
== 倧ãã ââ å°ãã ==
<big>[[wikt:granda|Granda]]<!--BRO2--> - (ã°ã©ã³ã) ââ [[wikt:malgranda|Malgranda]] - (ãã«ã°ã©ã³ã)</big>
<gallery>
File:Rostrhamus_sociabilis_sitting.jpg|Aglo estas granda birdo. (ããã¯å€§ãããšãã§ãã)
File:Tree Sparrow Japan Flip.jpg|Pasero estas malgranda birdo. (ãããã¯å°ãããšãã§ãã)
</gallery>
----<br>
== ããã ââ ããã ==
<big>[[wikt:peza|Peza]]<!--BRO5--> - (ããŒã¶) ââ [[wikt:malpeza|Malpeza]] - (ãã«ããŒã¶)</big>
<gallery>
File:Elefant_Tanzà nia.JPG|Elefanto estas peza. (ããã¯ãããã§ãã)
File:House_mouse.jpg|Muso estas malpeza. (ããã¿ã¯ãããã§ãã)
</gallery>
----<br>
== ããã ââ ã²ãã ==
<big>[[wikt:alta|Alta]]<!--BRO2--> - (ã¢ã«ã¿) ââ [[wikt:malalta|Malalta]] - (ãã«ã¢ã«ã¿)</big>
----<br>
== ãããã ââ ããªãã ==
<big>[[wikt:Äoja|Äoja]]<!--BRO2--> - (ãã§ãŒã€) ââ [[wikt:malÄoja|MalÄoja]] - (ãã«ãã§ãŒã€)</big>
----<br>
== ãªãã ââ ã¿ããã ==
<big>[[wikt:longa|Longa]]<!--BRO2--> - (ãã³ã¬) ââ [[wikt:mallonga|Mallonga]] - (ãã«ãã³ã¬)</big>
----<br>
== (ãããã)ã¯ãã ââ ããã ==
<big>[[wikt:rapida|Rapida]]<!--BRO2--> - (ã©ããŒã) ââ [[wikt:malrapida|Malrapida]] - (ãã«ã©ããŒã)</big>
----<br>
== (ãããã)ã¯ãã ââ ããã ==
<big>[[wikt:frua|Frua]]<!--BRO3--> - (ãã«ãŒã¢) ââ [[wikt:malfrua|Malfrua]] - (ãã«ãã«ãŒã¢)</big>
----<br>
== ããŸã ââ ã«ãã ==
<big>[[wikt:dolÄa|DolÄa]]<!--BRO3--> - (ãã«ãã£) ââ [[wikt:maldolÄa|MaldolÄa]] - (ãã«ãã«ãã£)</big>
----<br>
== ãã€ã ââ ãããã»ã€ããã ==
<big>[[wikt:varma|Valma]]<!--BRO3--> - (ãŽã¡ã«ã) ââ [[wikt:malvalma|Malvarma]] - (ãã«ãŽã¡ã«ã)</big>
----<br>
== ãµãšã ââ ã»ãã ==
<big>[[wikt:dika|Dika]]<!--BRO4--> - (ãã£ãŒã«) ââ [[wikt:maldika|Maldika]] - (ãã«ãã£ãŒã«)</big>
----<br>
== ããã ââ ããã ==
<big>[[wikt:kara|Kara]]<!--BRO4--> - (ã«ãŒã©) ââ [[wikt:malkara|Malkara]] - (ãã«ã«ãŒã©)</big>
----<br>
== ãããã ââ ããã ==
<big>[[wikt:hela|Hela]]<!--BRO4--> - (ããŒã©) ââ [[wikt:malhela|Malhela]] - (ãã«ããŒã©)</big>
----<br>
== ã²ãã ââ ããŸã ==
<big>[[wikt:vasta|Vasta]]<!--BRO5--> - (ãŽã¡ã¹ã¿) ââ [[wikt:malvasta|Malvasta]] - (ãã«ãŽã¡ã¹ã¿)</big>
----<br>
== ããããã ââ ããã ==
<big>[[wikt:mola|Mola]]<!--BRO5--> - (ã¢ãŒã©) ââ [[wikt:malmola|Malmola]] - (ãã«ã¢ãŒã©)</big>
----<br>
[[Category:ãšã¹ãã©ã³ã (ãŠã£ããžã¥ãã¢)|åèª ããã]]
| null |
2015-08-30T01:54:50Z
|
[] |
https://ja.wikibooks.org/wiki/Wikijunior:%E3%82%A8%E3%82%B9%E3%83%9A%E3%83%A9%E3%83%B3%E3%83%88%E3%81%9F%E3%82%93%E3%81%94/%E3%82%88%E3%81%86%E3%81%99
|
16,278 |
æ°äºåçèŠå第143æ¡
|
ã³ã³ã¡ã³ã¿ãŒã«æ°äºåçèŠå(å)(次)
(ç Žç£æç¶ããåçæç¶ãžã®ç§»è¡ã«äŒŽãå
±ç嵿š©ã®ç³åº)
|
[
{
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"tag": "p",
"text": "ã³ã³ã¡ã³ã¿ãŒã«æ°äºåçèŠå(å)(次)",
"title": ""
},
{
"paragraph_id": 1,
"tag": "p",
"text": "(ç Žç£æç¶ããåçæç¶ãžã®ç§»è¡ã«äŒŽãå
±ç嵿š©ã®ç³åº)",
"title": "æ¡æ"
},
{
"paragraph_id": 2,
"tag": "p",
"text": "",
"title": "æ¡æ"
},
{
"paragraph_id": 3,
"tag": "p",
"text": "",
"title": "解説"
},
{
"paragraph_id": 4,
"tag": "p",
"text": "",
"title": "åç
§æ¡æ"
}
] |
ã³ã³ã¡ã³ã¿ãŒã«æ°äºåçèŠåïŒåïŒïŒæ¬¡ïŒ
|
[[ã³ã³ã¡ã³ã¿ãŒã«æ°äºåçèŠå]]ïŒ[[æ°äºåçèŠå第142æ¡|å]]ïŒïŒ[[æ°äºåçèŠå第144æ¡|次]]ïŒ
==æ¡æ==
ïŒç Žç£æç¶ããåçæç¶ãžã®ç§»è¡ã«äŒŽãå
±ç嵿š©ã®ç³åºïŒ
;第143æ¡ã
#[[æ°äºåçæ³ç¬¬39æ¡|æ³ç¬¬39æ¡]]ïŒä»ã®æç¶ã®äžæ¢çïŒç¬¬3é
第äžå·ã«æ²ããè«æ±æš©ãæããè
ã¯ãåçæç¶éå§ã®æ±ºå®ããã£ãããšãç¥ã£ããšãã¯ãéããã«ãåå·ã®èŠå®ã«ããå
±ç嵿š©ãšãããåœè©²è«æ±æš©ãæããæšãåçåµåè
çã«ç³ãåºããã®ãšããã
#[[æ°äºåçèŠå第2æ¡|第2æ¡]]ïŒç³ç«ãŠã®æ¹åŒçïŒç¬¬2é
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==解説==
*æ³ç¬¬39æ¡ïŒä»ã®æç¶ã®äžæ¢çïŒ
==åç
§æ¡æ==
{{stub}}
[[category:æ°äºåçèŠå|143]]
| null |
2011-07-23T02:45:54Z
|
[
"ãã³ãã¬ãŒã:Stub"
] |
https://ja.wikibooks.org/wiki/%E6%B0%91%E4%BA%8B%E5%86%8D%E7%94%9F%E8%A6%8F%E5%89%87%E7%AC%AC143%E6%9D%A1
|
16,279 |
æ°äºå·è¡èŠå第31æ¡
|
æ³åŠ>æ°äºæ³>ã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡èŠå
(ç©ä»¶æçްæžã®åãã®å眮ãç)
|
[
{
"paragraph_id": 0,
"tag": "p",
"text": "æ³åŠ>æ°äºæ³>ã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡èŠå",
"title": ""
},
{
"paragraph_id": 1,
"tag": "p",
"text": "(ç©ä»¶æçްæžã®åãã®å眮ãç)",
"title": "æ¡æ"
},
{
"paragraph_id": 2,
"tag": "p",
"text": "",
"title": "åç
§æ¡æ"
}
] |
æ³åŠïŒæ°äºæ³ïŒã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡èŠå
|
[[æ³åŠ]]ïŒ[[æ°äºæ³]]ïŒ[[ã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡èŠå]]
==æ¡æ==
ïŒç©ä»¶æçްæžã®åãã®å眮ãçïŒ
;第31æ¡
#ç©ä»¶æçްæžã®åãã®å眮ãã¯ã売åŽã®å®æœã®æ¥ã®äžé±éåãŸã§ã«ããªããã°ãªããªãã
#å·è¡è£å€æã¯ãäžè¬ã®é²èЧã«äŸããããã«ãçŸæ³èª¿æ»å ±åæžåã³è©äŸ¡æžã®åããç©ä»¶æçްæžã®åããšå
±ã«å·è¡è£å€æã«åã眮ããªããã°ãªããªãã
#ç©ä»¶æçްæžã®åãçãåã眮ããããšãã¯ãè£å€ææžèšå®ã¯ããã®æšåã³åã眮ãããå¹Žææ¥ãèšé²äžæããã«ããªããã°ãªããªãã
==解説==
==åç
§æ¡æ==
*[[æ°äºå·è¡æ³ç¬¬62æ¡]]ïŒç©ä»¶æçްæžïŒ
{{stub}}
[[category:æ°äºå·è¡èŠå|31]]
| null |
2011-07-23T04:49:57Z
|
[
"ãã³ãã¬ãŒã:Stub"
] |
https://ja.wikibooks.org/wiki/%E6%B0%91%E4%BA%8B%E5%9F%B7%E8%A1%8C%E8%A6%8F%E5%89%87%E7%AC%AC31%E6%9D%A1
|
16,280 |
æ°äºå·è¡æ³ç¬¬62æ¡
|
æ³åŠ>æ°äºæ³>ã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡æ³
(ç©ä»¶æçްæž)
|
[
{
"paragraph_id": 0,
"tag": "p",
"text": "æ³åŠ>æ°äºæ³>ã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡æ³",
"title": ""
},
{
"paragraph_id": 1,
"tag": "p",
"text": "(ç©ä»¶æçްæž)",
"title": "æ¡æ"
},
{
"paragraph_id": 2,
"tag": "p",
"text": "",
"title": "å€äŸ"
}
] |
æ³åŠïŒæ°äºæ³ïŒã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡æ³
|
[[æ³åŠ]]ïŒ[[æ°äºæ³]]ïŒ[[ã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡æ³]]
==æ¡æ==
ïŒç©ä»¶æçްæžïŒ
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ãèšèŒããç©ä»¶æçްæžãäœæããªããã°ãªããªãã
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#:äº ãäžåç£ã«ä¿ãæš©å©ã®ååŸåã³ä»®åŠåã®å·è¡ã§å£²åŽã«ãããã®å¹åã倱ããªããã®
#:äž ã売åŽã«ããèšå®ããããã®ãšã¿ãªãããå°äžæš©ã®æŠèŠ
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ãåœè©²ç©ä»¶æçްæžã®å
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#åäºé
ã®èŠå®ã«ããè£å€ææžèšå®ã®åŠåã«å¯ŸããŠã¯ãå·è¡è£å€æã«ç°è°ãç³ãç«ãŠãããšãã§ããã
#[[æ°äºå·è¡æ³ç¬¬10æ¡|第10æ¡]]第6é
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ã®èŠå®ã«ããç°è°ã®ç³ç«ãŠããã€ãå Žåã«ã€ããŠæºçšããã
==解説==
*第10æ¡(å·è¡æå)
==åç
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*[[æ°äºå·è¡èŠå第31æ¡]]ïŒç©ä»¶æçްæžã®åãã®å眮ãçïŒ
==å€äŸ==
*[http://www.courts.go.jp/search/jhsp0030?hanreiid=55874&hanreiKbn=02 â売買代éè¿éç](æé«è£å€äŸ âå¹³æ8幎01æ26æ¥ïŒ[[æ°æ³ç¬¬566æ¡]]1é
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----
{{stub}}
[[category:æ°äºå·è¡æ³|62]]
| null |
2011-07-23T04:53:23Z
|
[
"ãã³ãã¬ãŒã:Stub"
] |
https://ja.wikibooks.org/wiki/%E6%B0%91%E4%BA%8B%E5%9F%B7%E8%A1%8C%E6%B3%95%E7%AC%AC62%E6%9D%A1
|
16,281 |
æ°äºå·è¡æ³ç¬¬26æ¡
|
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(å·è¡æã®ä»äž)
|
[
{
"paragraph_id": 0,
"tag": "p",
"text": "æ³åŠ>ã³ã³ã¡ã³ã¿ãŒã«æ°äºèšŽèšæ³>ã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡æ³",
"title": ""
},
{
"paragraph_id": 1,
"tag": "p",
"text": "(å·è¡æã®ä»äž)",
"title": "æ¡æ"
}
] |
æ³åŠïŒã³ã³ã¡ã³ã¿ãŒã«æ°äºèšŽèšæ³ïŒã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡æ³
|
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==æ¡æ==
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# å·è¡æã®ä»äžã¯ã嵿š©è
ãåµåè
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==解説==
==åç
§æ¡æ==
----
{{ååŸ
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|[[ã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡æ³#2|第2ç« åŒ·å¶å·è¡]]<br>
[[ã³ã³ã¡ã³ã¿ãŒã«æ°äºå·è¡æ³#2-1|第1ç¯ ç·å]]<br>
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|[[æ°äºå·è¡æ³ç¬¬27æ¡]]<br>ïŒå·è¡æã®ä»äžïŒ
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{{stub}}
[[category:æ°äºå·è¡æ³|026]]
| null |
2014-05-02T21:50:11Z
|
[
"ãã³ãã¬ãŒã:ååŸ",
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¥ããä»ã®æ°æãåŒãé£ããŠããŸãããæ°æç³»çµ±äžæã®ãã«ãªäººããã®é ãæ±æ¹ããã¡ãœãã¿ãã¢åéšã«ãã£ãŠããŸããããã®åŸããã«ãªäººã¯ä»ã®å°åã«ç§»åããã€ã³ãã»ãšãŒãããèªæãç¯ããçåœã«äœã人ã
ã®éèŠãªäžéšãšãªããŸãããã€ã³ãã»ãšãŒãããèªç³»æ°æã®è»éã¯ã銬(ãªãªãšã³ãã§åç»å Ž)ãåŒãæŠè»ã§æ§æãããŠããŸãããåªããæ©ååã¯ãå
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"title": "ã€ã³ã=ãšãŒãããèªç³»æ°æã®é²åº"
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"text": "ãŸããçŽå
å19äžçŽé ãããã¿ã€ãã®äžæŽŸãå°ã¢ãžã¢ã®ã¢ãããªã¢é«åã«ç§»äœããŠãå
äœè«žæ°æãšãšãã«ããã¿ã€ãçåœã建åœããŸãããçŽå
å1650幎é ã«ã¯ããããã¥ã·ã£ãéŠéœãšãã匷åãªåžåœã«æé·ããŸããããã€ã人ã®ããŒãŽã»ãŠã£ã³ã¯ã©ãŒã¯ã1905幎ãã1906幎ã«ãããŠãåœæãªã¹ãã³åžåœã ã£ãã¢ãããªã¢é«åã®ãã¢ãºã³ã€éºè·¡ãæããŸããã圌ã¯ãããã«ããã¿ã€ãçåœã®éŠéœãããã¥ã·ã£ãååšãããšå€æããŸãããããã¿ã€ãã®ç ç©¶ã¯ããããŠãã¢ãºãã§ã€éºè·¡ããçºèŠãããå€ãã®ç²åæ¿ãè§£èªããç ç©¶ãé²ããããã«ãªããŸãããçŸåšãæ¥æ¬ãããå°ã¢ãžã¢ã«èª¿æ»å£ã掟é£ãããçºæèª¿æ»ãè¡ã£ãŠããŸãã",
"title": "ã€ã³ã=ãšãŒãããèªç³»æ°æã®é²åº"
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"tag": "p",
"text": "çŽå
å16äžçŽåãã«ã¯ããããã³ç¬¬1çæãšæŠãããããæ»
ãŒããŸãããçŽå
å14äžçŽãåžåœã®æçæã«ã¯åäžãããã¿ã³ãã»ãšãžãããšæŠããŸããããã®äžã§æãæåãªã®ã¯ãçŽå
å13äžçŽåé ã«èµ·ãã£ãã«ãã·ã¥ã®æŠãã§ããã«ãã·ã¥ã®æŠãã§ã¯ãåäžããŠãããšãžããæ°çåœæä»£ã®ã©ã¡ã»ã¹2äžãšãã·ãªã¢ã®æ¯é
æš©ãããã£ãŠæŠããŸãããæŠããåŒãåãã«çµãã£ãåŸãäž¡åœã¯å¹³åæ¡çŽãç· çµããŸãããããã¯ãçŸåšãæ®ã2åœéã®æ¡çŽãšããŠã¯æãå€ãæ¡çŽã§ããéŠ¬ãæŠè»ãšãšãã«ãé補æŠåšã䜿ããè»éã匷ãããŸãããçŽå
å12äžçŽåé ãå°äžæµ·æ±éšã襲ã£ãæ°æå€§ç§»åã®æ³¢ã®äžã§ããã«ã«ã³åå³¶ããæ¥ãæ°æã«ãã£ãŠæ»
ãŒãããŸããããããããã以éãããã¿ã€ãã®è£œéæè¡ã¯ãªãªãšã³ãåå°ã«åºãŸããŸããã",
"title": "ã€ã³ã=ãšãŒãããèªç³»æ°æã®é²åº"
},
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"tag": "p",
"text": "ãããã³ç¬¬1çæãæ»
ãã åŸãæ±ã®å±±å°ããã«ãã·ãŒã人ãšããå¥ã®ã€ã³ãã»ãšãŒãããèªæããã£ãŠããŠããããã³ç¬¬äžçæãšããçåœãç¯ããŸããããã®çåœã¯çŽ400幎ã«ãããã¡ãœãã¿ãã¢åéšãæ¯é
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å15äžçŽããæ¬¡ã®äžçŽã®åã°ãŸã§ãã¡ãœãã¿ãã¢åéšãšã·ãªã¢åéšã«åŒ·ãå¢åãèªã£ãŠããŸãããçŽå
å2å幎ã®äžé ããªãªãšã³ãã§ã¯ãšãžããã®æ°çåœãªã©ãæ§ã
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å1200幎é ã倧移åãæ±å°äžæµ·å°æ¹ã襲ããšãæ¿æ²»ç¶æ³ã¯ããã«æ··ä¹±ããŸããããããããã®æ··ä¹±ã®äžããæ°ããªå¢åãçãŸãããªãªãšã³ãã«ã¯æ°ããç§©åºãçãŸãå§ããŸããã",
"title": "ã€ã³ã=ãšãŒãããèªç³»æ°æã®é²åº"
},
{
"paragraph_id": 5,
"tag": "p",
"text": "ã¡ãœãã¿ãã¢ã§ã¯ãåå°ãåéœåžã®å®è·ç¥ãèªç¶ç¥ãç¥ãå€ç¥æãæ ¹ä»ããŠããŸãããããããåªå¢ãªæ°æããã°ãã°å€ãã£ããããä¿¡ä»°ãããæé«ç¥ãå€ãããŸããããããã³ç¬¬1çæã®æä»£ã«ã¯ããããã³ãšããéœåžã®ç¥ã§ãããã«ãã¥ã¯ãåœå®¶ç¥ãšãããŸããããŸããã·ã¥ã¡ãŒã«ã®åªãã宿æåŠ(ç¥è©±ãã®ã«ã¬ã¡ã·ã¥åäºè©©)ã¯ãã»ã èªç³»è«žæ°æã®éã§ãåºãŸãã倧ããªåœ±é¿ãåããŸããã",
"title": "ã¡ãœãã¿ãã¢ã®æå"
},
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"tag": "p",
"text": "ã®ã«ã¬ã¡ã·ã¥ã¯ããŠã«ã¯ç¬¬1çææä»£ã®æ¬åœã®çã ã£ããšèããããŠããŸããèå€åŠçã«èšŒæãããŠããªããŠããåŸäžã®èšãäŒãã§ã圌ãããã«åæ¢ã§ãå€ãã®æŠãã«åå©ããå倧ãªçãªã®ããå€ãã®ç©èªãšããŠäŒããŠããŸãããã®ã«ã¬ã¡ã·ã¥åäºè©©ãã¯ãç¥ãšäººã
ã®äº€æµãè±éã®å§¿ãç©èªããŸãã",
"title": "ã¡ãœãã¿ãã¢ã®æå"
},
{
"paragraph_id": 7,
"tag": "p",
"text": "圌ã¯å人ã®ãšã³ããã¥ãšåéºã®æ
ã«åºãããã¬ããã³æã®æ£®ã管çããŠãããã³ããããç¥ããããªãšèšã£ãã«ããããããæ®ºããŸãã(森ãæãåºããææã«å
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ã諊ããŸãããæŽªæ°Žããéããããã«ç®±èãäœããæ°žé ã«çãããŠãããã·ã¥ãã ã«åºäŒããæ°žé ã«çãããããšããè¬èãæã«å
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"title": "ã¡ãœãã¿ãã¢ã®æå"
},
{
"paragraph_id": 8,
"tag": "p",
"text": "ã¡ãœãã¿ãã¢ã§ã¯æ§ã
ãªæè¡ãæåãäœããããããåŸã«ä»ã®ææã®åºç€ãšãªããŸãããã¡ãœãã¿ãã¢ã§ã¯ã3000幎åããæ¥åœ¢æåã䜿ãããŠããŸããæãåºããç²åæ¿ã«ãéå©ãªèŠã®èã§äœã£ãç¹æ®ãªãã³ã§æŒããŠæžããŸããç²åæ¿ã¯ãä¿ç®¡ããå¿
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"title": "ã¡ãœãã¿ãã¢ã®æå"
},
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"tag": "p",
"text": "ãŸããå æè¡ãè¡ãããã€èŸ²äœæ¥ãããã°ããããç¥ãå¿
èŠããã£ãããã倩æã»æŠæ³ã»æ°åŠã»èŸ²åŠãçºå±ããŠãããŸãããæã®åãæ¹ãããšã«ããå€ªé°æŠã¯ã1å¹Žã®æ¥æ°ã354æ¥ã§ããããã§ã¯ãå®éã®å£ç¯ãšåããŸãããããã§ãéæãäœãã倪é°å€ªéœæŠã«å€æŽããŸãããã¡ãœãã¿ãã¢ææã¯ãå
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"title": "ã¡ãœãã¿ãã¢ã®æå"
}
] |
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2022-12-01T14:18:50Z
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"text": "人é¡ãç³åšã䜿ãå§ããææã¯ãä»ããããã250äžå¹Žåã®ãã(æŽæ°äžã§ãã)ãšèããããŠããã ç³åšã«ãæã¡æ¬ ããŠã€ãã£ãã ãã®æè£œç³åš(ã ãããã£ã)ã®ã¿ã䜿çšããŠããæ§ç³åšæä»£(ãã
ããã£ããã ã)ããç³åšæä»£ã®äžã§ãæãå€ãã",
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ãããã)ã§ãæŽæ°äžã«å ç©ãã颿±ããŒã å±€ããæè£œç³åšãçžæ²¢å¿ æŽ(ãããã ãã ã²ã)ãçºèŠããããããŠ1949幎ã«ãåŠè¡èª¿æ»ãè¡ãããããããã®èª¿æ»ã«ãããæ¥æ¬ã«ãæ§ç³åšæä»£ããã£ãããšã蚌æãããæ¥æ¬å²äžã®å®èª¬ãèŠãããšãšãªã£ãã",
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"title": "æ§ç³åšæä»£"
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"tag": "p",
"text": "ããã§ã¯ååãšçšéã玹ä»ãããè³æéãªã©ã§å®ç©ã®åçã確èªããŠããã ãããã",
"title": "æ§ç³åšæä»£"
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"text": "人骚ã¯3çš®é¡èŠããšãã°åé¡ãªãã æ²çžçã®æž¯å·äºº(ã¿ãªãšãããã)ã»å±±äžçºæŽäºº(ããŸããã¡ããã©ããã) é岡çã®æµå人(ã¯ãŸãããã)ã§ããããããã®äººéªšã¯ããããæ°äººæ®µéã§ããã3äžå¹ŽåãŸã§ã®äººéªšã§ããã",
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"title": "æ§ç³åšæä»£"
},
{
"paragraph_id": 12,
"tag": "p",
"text": "ä»ããããã1äžæ°å幎åããã®æŽæ°äžæ«æãããå°çã®æ°åãæž©æåããŠæµ·é¢ãäžæããããã«ããæ¥æ¬åå³¶ã圢æãããã(çŽ1äžå¹Žå)",
"title": "çžææä»£"
},
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"tag": "p",
"text": "æ€ç©ã¯ãæ±æ¥æ¬ã§ã¯èœèåºèæš¹æãåºãããè¥¿æ¥æ¬ã§ã¯ç
§èæš¹æãåºãã£ãããã®æ£®æã®å€åã«ãšããªãããã³ã°ãªãã¯ã«ããã¯ãªãªã©ã®æšã®å®ããã€ãã€ã¢ãªã©ã®æ ¹èé¡(ãããããã)ãè±å¯ã«ãªã£ãã",
"title": "çžææä»£"
},
{
"paragraph_id": 14,
"tag": "p",
"text": "人é¡ã¯ 磚補ç³åš(ãŸãããã£ã)ãååšãåŒç¢ ãæã«ãçæŽ»åºæ¿ãåµãäžããŠãã£ãããã®æä»£ã®ååšã®æš¡æ§ã«ã¯ãçžãå転ãããŠååšã«ã€ããæš¡æ§ãå€ãããã®ããããã®æä»£ã®ååšã®ããšãçžæååš(ãããããã©ã)ãšèšãããŸãããã®æä»£ãçžææä»£ãšããã",
"title": "çžææä»£"
},
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"paragraph_id": 15,
"tag": "p",
"text": "åç©ã¯ããã³ã¢ã¹ãªã©ã®å€§ååç©ã¯ãã§ã«çµ¶æ»
ããŠãããã·ã«ãã€ãã·ã·ããŠãµã®ãªã©ã®æ¯èŒçå°åã§ä¿æãªåç©ãå€ãã£ãããã®ãããªä¿æãªåç©ãç©ãã®ã«ãåŒç¢ãé©ããŠãããç§çã¯è¡ãããŠããªãããŸããæ¬æ ŒçãªèŸ²èã¯è¡ãããŠããªãã",
"title": "çžææä»£"
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"tag": "p",
"text": "ãŸããååšã¯è²¯èµ(ã¡ããã)ã®ä»ã«ããé£ç©ã®ç
®çã(ã«ãã)ã«ã䜿ãããŠããããã§ãããæšã®å®ã®ã¢ã¯æãããç£èã®ç
®æ²žãªã©ã«ã䜿ãããããã§ããã",
"title": "çžææä»£"
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"text": "ãŸãã骚è§åš(ãã£ããã)ãšããåç©ã®éªšãè§ãéãé£ãéã«äœ¿çšããŠããã",
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"tag": "p",
"text": "çžæååšã®ç¹åŸŽãšã㊠çžç®æš¡æ§ é»è€è²(äœæž©ã§çŒããŠãããã) åæã§ããã ãæããããã",
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"tag": "p",
"text": "æšã®å®ãªã©ã«ããå®äœããŠåŸãããé£æãæ®åãããããã人ã
ã¯ç«ªç©Žäœå±
(ããŠã㪠ãã
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"title": "çžææä»£"
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"text": "ãŸã亀æãçãã§ãã£ãããšãåãã£ãŠããã",
"title": "çžææä»£"
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"tag": "p",
"text": "èªç¶çŸè±¡ã«éåšãèªããåªè¡(ãã
ãã
ã€)çãªææ³(ããããã¢ãããºã )ããã£ããšèããããŠããã女æ§ãããã©ã£ãåå¶(ã©ãã)ããç·æ§ã®çæ®åš(ããããç·æ ¹)ãããã©ã£ãç³æ£(ãããŒã)ããããææ¯(ã°ã£ã)ããæäººåŒãå©å§»ãªã©ã®ãšãã«ééå瀌ãšããŠæ¯ãæã颚ç¿ã ã£ããæ»è
ãåè¬ãããšãã«æ»äœã®æè¶³ãããããå±è¬(ãã£ãã)ããã£ãããŸãç°ç¶åç³(ããããããã£ãããç§ç°çã®å€§æ¹¯ãããããã)ãã¢ãããºã ã®äžã€ã ãšèããããŠããã",
"title": "çžææä»£"
},
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"tag": "p",
"text": "çžææä»£ã§æåãªéºè·¡ã¯ã鿣®çã«ããäžå
äžžå±±éºè·¡(ãããªããŸãããŸããã)ã§ããã",
"title": "çžææä»£"
},
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"tag": "p",
"text": "身åã®å·®ã¯ãããŸãç¡ãã£ãããã§ããã寿åœã¯çãã30æ³ããããŸã§ãã ã£ãããã§ããã",
"title": "çžææä»£"
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[[category:äŒç€Ÿæ³æœè¡èŠå|179]]
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2011-07-26T02:56:02Z
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16,289 |
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"text": "ãŸãå°åããšã«æ Œå·®ãçãŸãããããã¯å¢ãèŠãã°äžç®çç¶ã§ãã£ãã",
"title": "匥çæä»£"
},
{
"paragraph_id": 22,
"tag": "p",
"text": "çžææä»£ã®ããã¯æ»è
ã®å€ãã«å±è¬ãè¡ã£ãŠãããã匥çæä»£ã«ãªã䌞å±è¬(ãããŠããã)ãè¡ãããšãå€ããªã£ãã",
"title": "匥çæä»£"
},
{
"paragraph_id": 23,
"tag": "p",
"text": "ãæŒ¢æžãå°çå¿",
"title": "äžåœå²æžããã¿ãæ¥æ¬"
},
{
"paragraph_id": 24,
"tag": "p",
"text": "ããã¯ã挢æžãå°çå¿(ãããããã¡ãã)(èè
:çåº)ã®æç²ããæŒ¢æããæ¥æ¬èªã«æžãäžããæã§ããã(åæžã¯æŒ¢æ)",
"title": "äžåœå²æžããã¿ãæ¥æ¬"
},
{
"paragraph_id": 25,
"tag": "p",
"text": "ã€ãŸãã",
"title": "äžåœå²æžããã¿ãæ¥æ¬"
},
{
"paragraph_id": 26,
"tag": "p",
"text": "ãšããããšã§ããã",
"title": "äžåœå²æžããã¿ãæ¥æ¬"
},
{
"paragraph_id": 27,
"tag": "p",
"text": "ãåŸæŒ¢æžãæ±å€·äŒ(ãããããããšããã§ã)",
"title": "äžåœå²æžããã¿ãæ¥æ¬"
},
{
"paragraph_id": 28,
"tag": "p",
"text": "ããã¯ãåŸæŒ¢æžãæ±å€·äŒ(ãããããããšããã§ã)ã®æç²ã§ãã(èè
:èæãåæžã¯æŒ¢æ)ã",
"title": "äžåœå²æžããã¿ãæ¥æ¬"
},
{
"paragraph_id": 29,
"tag": "p",
"text": "å
容ã¯ã»ã»ã»",
"title": "äžåœå²æžããã¿ãæ¥æ¬"
},
{
"paragraph_id": 30,
"tag": "p",
"text": "ãšãã話ã§ããã",
"title": "äžåœå²æžããã¿ãæ¥æ¬"
},
{
"paragraph_id": 31,
"tag": "p",
"text": "",
"title": "äžåœå²æžããã¿ãæ¥æ¬"
},
{
"paragraph_id": 32,
"tag": "p",
"text": "äžåœå€§éžã§ã¯åŸæŒ¢ã220å¹Žã«æ»
ã³ã220幎ããã«ã¯é(ã)ã»è(ããã)ã»å(ã)ã®3ã«åœã䞊ã³ç«ã€äžåœæä»£(ãããã ãã ã)ã«ãªã£ãŠããã",
"title": "éªéЬå°åœ"
},
{
"paragraph_id": 33,
"tag": "p",
"text": "äžåœã®æŽå²æžãäžåœå¿ã(ããããã)ã®ãã¡ã®ãéã«ã€ããŠã®æŽå²æžã®ãéå¿ã(ãã)ã«ããå人ã«ã€ããŠã®èšè¿°(å人äŒ(ãããã§ã))ã«ãããšã3äžçŽã®å§ãããã®æ¥æ¬ã§ã¯ãå°åœã©ããã®äºããå€ãã£ããã30ãåœã»ã©ã®å°åœãå°åœã©ããã®å
±åã®å¥³çãšããŠãéªéЬå°åœ(ããŸãããã)ã®å匥åŒ(ã²ã¿ã)ãšãã女çãç«ãŠãŠé£åããæ¥æ¬ã®æŠä¹±ããããŸã£ããšãããå匥åŒã¯ã30ãåœã»ã©ã®åœãããããããšããã",
"title": "éªéЬå°åœ"
},
{
"paragraph_id": 34,
"tag": "p",
"text": "éªéЬå°åœã®å匥åŒã¯ã239幎ã«éã«äœ¿è
ãããããéã®çåžãããã芪éåçã(ãããããã)ã®ç§°å·ããããããŸãéå°ãšãé
é¡100æãããã£ãããšããå人äŒã«èšãããŠããã",
"title": "éªéЬå°åœ"
},
{
"paragraph_id": 35,
"tag": "p",
"text": "å匥åŒã¯æ©å¹Žãç奎åœ(ããªãã)ãšæŠã£ããšãããããã®çŽåŸã®ããã®247幎ã«å匥åŒã¯äº¡ããªã£ãã人ã
ã¯ãå匥åŒã®ããã®å€§ããªå¢ãã€ãã£ãããã®ã®ã¡ç·ã®çãç«ã£ãããåœå
ãä¹±ãããããå匥åŒã®åæã§ãã13æ³ã®å£±äž(ãã)ã女çã«ãªã£ãŠæŠä¹±ãåãŸã£ãã壱äžã¯ãéã«ããã£ãæã«å¯ŸããŠäœ¿è
ã266幎ã«éã£ããéå¿å人äŒã«ãããšãæã®éœã®æŽéœã«ãåã®å¥³çã»å£±äžããã®äœ¿è
ãæ¥ãããšããµããªããšãæžãããŠããã",
"title": "éªéЬå°åœ"
},
{
"paragraph_id": 36,
"tag": "p",
"text": "ãã®å£±äžããã®äœ¿è
ã®èšè¿°ã®ããšããã°ããäžåœã®æç®ã«ã¯åã«ã€ããŠã®èšè¿°ã¯ç»å Žããªããªãããã266幎ãã150幎éã»ã©ã®åã«ã€ããŠã®è©³çްã¯äžæã§ããã",
"title": "éªéЬå°åœ"
},
{
"paragraph_id": 37,
"tag": "p",
"text": "éªéЬå°åœã®äœçœ®ããã©ãã«ãã£ãã®ãã¯ãçŸåšã§ãäžæã§ãããåŠèª¬ã§ã¯ãè¿ç¿å°æ¹ã®å€§å(ããŸãš)ã«ããšãã説ãšä¹å·èª¬ããæåãªèª¬ã§ããã",
"title": "éªéЬå°åœ"
},
{
"paragraph_id": 38,
"tag": "p",
"text": "è¿ç¿å°æ¹ã«ããšãã説ã®å Žåãã®ã¡ã®ã€ããçæš©ã®æ¯äœãéªéЬå°åœã ã£ããšãããããªå¯èœæ§ãé«ããä¹å·ããè¿ç¿ãŸã§ã®ç¯å²ããµããé£åæ¿æš©ããã£ãããšã«ãªãããã£ãœããä¹å·èª¬ãåã£ãå ŽåãéªéЬå°åœã¯æ¯èŒçå°èŠæš¡ãªå°æ¹æ¿æš©ã®é£åã ãšããããšã«ãªãã",
"title": "éªéЬå°åœ"
},
{
"paragraph_id": 39,
"tag": "p",
"text": "ä¹å·èª¬ãåãããè¿ç¿èª¬ãåããã§ãéªéЬå°åœãšã€ããçæš©ã«ã€ããŠã®èãæ¹ãã倧ããç°ãªãã",
"title": "éªéЬå°åœ"
},
{
"paragraph_id": 40,
"tag": "p",
"text": "ãã®æä»£ã®æ¥æ¬ã«ã¯ãéçŽã奎é·ããçãŸã§ããã£ãããšããå人äŒã®èšè¿°ããåãã£ãŠããã",
"title": "éªéЬå°åœ"
},
{
"paragraph_id": 41,
"tag": "p",
"text": "éå¿å人äŒã«ã¯ãã€ãã®ãããªããšãæžãããŠããã(äžéšçç¥)",
"title": "éå¿å人äŒ"
},
{
"paragraph_id": 42,
"tag": "p",
"text": "",
"title": "éå¿å人äŒ"
},
{
"paragraph_id": 43,
"tag": "p",
"text": "éå¿å人äŒã¯ãæ£åŒåã¯ãäžåœå¿ãã®ãéæžã(ããã)ã®æ±å€·äŒã®å人æ¡ããäžåœå¿ãã¯äžäžçŽã«æ®(ãã)ã®é³å¯¿(ã¡ããã
)ã«ãã£ãŠç·šçº(ãžããã)ãããã",
"title": "éå¿å人äŒ"
}
] | null |
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2011-08-15T03:14:33Z
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16,305 |
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2011-08-15T03:28:46Z
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16,306 |
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2011-08-15T03:33:33Z
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2011-08-15T03:37:17Z
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[
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"tag": "p",
"text": "è£å€æ(ããã°ããããè±:court)ã«ã¯ãæé«è£å€æ(ãããã ããã°ããã)ãšäžçŽè£å€æ(ããã
ã ããã°ããã)ããããŸãã",
"title": "è£å€ã®åºæ¬"
},
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"text": "äžçŽè£å€æã«ã¯ãé«çè£å€æ(ãããšã ããã°ããã)ã»å°æ¹è£å€æ(ã¡ã»ã ããã°ããã)ã»å®¶åºè£å€æ(ããŠã ããã°ããã)ã»ç°¡æè£å€æ(ããã ããã°ããã)ã®4çš®é¡ããããŸãã",
"title": "è£å€ã®åºæ¬"
},
{
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"tag": "p",
"text": "è£å€ã¯ããã®äºä»¶ã®å
容ã«ãã£ãŠãå°æ¹è£å€æ(ã¡ã»ã ããã°ããã)ãå®¶åºè£å€æãç°¡æè£å€æã®ãã¥ãããã第äžå¯©(ã ã ãã£ãã)ãšãªããŸãããŸããè£å€ã¯äžåãŸã§åããããšãã§ããŸããããã äžå¯©å¶(ãããããã) ãšãããè£å€ãæ
éã«è¡ãããšã§äººæš©ãå®ãããã®å¶åºŠã§ãã",
"title": "è£å€ã®åºæ¬"
},
{
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"tag": "p",
"text": "ãæ§èšŽãã¯ããããããšèªãã (â» ãå蚎ã(ããã)ãšã¯éãã®ã§ãééããªãããã«ããªããå蚎ã(ããã)ãšã¯ãç¯çœªã®è¢«å®³ãåãã被害è
ããèŠå¯ãªã©ã®ææ»æ©é¢ã«ãç¯äººã®åŠçœ°ã®ããã®ææ»ãåãç· ãŸãã(èŠå¯ãªã©ã«)æ±ããããšããå蚎ãã«ã€ããŠã¯ç¯å²å€ãªã®ã§èŠããªããŠããããå蚎ãã ãšãèŠå¯ã®ç®¡èœ(ãããã€)ãªã®ã§ãè£å€æãšã¯ç®¡èœãéãã)",
"title": "è£å€ã®åºæ¬"
},
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"tag": "p",
"text": "ãäžåãã¯ããããããããšèªãã",
"title": "è£å€ã®åºæ¬"
},
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"tag": "p",
"text": "",
"title": "è£å€ã®åºæ¬"
},
{
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"tag": "p",
"text": "ãªããã©ã®è£å€ããååãšããŠå
¬éãããŠãããåèŽ(ãŒãã¡ãã)ã§ããŸããæ¥æ¬åœæ²æ³ç¬¬82æ¡ã«ããè£å€ãååãšããŠå
¬éããããšãå®ããããŠããŸãããŸããåèŽã¯ãç¡æã§ãã",
"title": "è£å€ã®åºæ¬"
},
{
"paragraph_id": 7,
"tag": "p",
"text": "ãã ããåèŽåžæè
ãããããããå Žåã¯ãããåŒããªã©ã®æœéž(ã¡ã
ããã)ã§ãåèŽã§ãã人ãéžã°ããŸãã",
"title": "è£å€ã®åºæ¬"
},
{
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"tag": "p",
"text": "",
"title": "è£å€ã®åºæ¬"
},
{
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"tag": "p",
"text": "è£å€ã¯ãéåžžã¯å€æ±ºã確å®ããå Žåã¯ãããã§è£å€ã¯çµããã§ããããäŸå€çã«ã倿±ºç¢ºå®åŸã§ããæ°ãã蚌æ ãçºèŠããããªã©ããŠãè£å€ã®å€æ±ºã®åæã«ãªã£ã蚌æ ã«é倧ãªèª€ããããå Žåãªã©ãè£å€ã«é倧ãªééãããã£ããšèªããããå Žåã«ã¯ãè£å€ããããªããäºãåºæ¥ãããã®ããçŽãã®è£å€ã å審(ãããã) ãšèšããå審ãèŠæ±ããããšãåå¯©è«æ±(ãããã ãããã
ã)ãšããã",
"title": "è£å€ã®åºæ¬"
},
{
"paragraph_id": 10,
"tag": "p",
"text": "ãã€ãŠæ»åã®å€æ±ºãåãã人ããå審ã«ããç¡çœªãšãªã£ãäŸããããã€ããããŸãã",
"title": "è£å€ã®åºæ¬"
},
{
"paragraph_id": 11,
"tag": "p",
"text": "è£å€ãæ
åœããè£å€å®ã«å¯ŸããŠåœäŒãå
é£ãªã©å€éšã®åã圱é¿ããããŒãããšã®ãªãããã«ãè£å€å®ã¯èªãã®è¯å¿ã«åŸããæ²æ³ããã³æ³åŸã«ã®ã¿ææãããããšã åžæ³æš©ã®ç¬ç«(ãã»ããã ã® ã©ãã〠ãè±:independence of judicial ) ãšãããŸãã",
"title": "åžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 12,
"tag": "p",
"text": "è£å€æã«ã¯ãå
·äœçãªè£å€ã®éã«ãæ³åŸãæ²æ³ã«éåããŠãªãã倿ã§ããæš©éãããããã®æš©éã éæ²ç«æ³å¯©æ»æš©(ããããã£ãœã ããããããè±:judicial review) ãšèšããŸãã(æ²æ³81æ¡)",
"title": "åžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 13,
"tag": "p",
"text": "æé«è£å€æã¯ãæ²æ³ã®å¯©æ»ã«ã€ããŠãæçµçãªæš©éãæã£ãŠããã®ã§ ãæ²æ³ã®çªäººã(ãããœãã® ã°ãã«ã) ãšèšãããã",
"title": "åžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 14,
"tag": "p",
"text": "ãéã®è²žãåãã§ã貞ããéãè¿ããŠããããªãå Žåããåå°ã®ããããšãªã©ã®ãããªã人ãšäººãšã®æ³çãªäºãããã€ããããããã¯ãäŒæ¥ãšäººãäŒæ¥ãšäŒæ¥ãšã®æ³çãªäºãããã€ããã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 15,
"tag": "p",
"text": "æ°äºè£å€ã§èšŽããåŽãåå(ãããããè±:plaintiff ãã¬ã³ãã£ã)ãšèšãã蚎ããããåŽã被å(ã²ãããè±:defendant ãã£ãã§ã³ãã³ã)ãšããã 被åã¯ããã®æç¹ã§ã¯ããã£ããŠç¯çœªã®ç¯äºº(ã¯ãã«ããè±:culprit ã«ã«ããªã)ã§ããªããã°ãç¯çœªã®ããããã®ãã容çè
(ããããããè±:ãµã¹ãã¯ã)ã§ããããŸããã 被åã®ç«å Žãšãç¯çœªãšã¯ãç¡é¢ä¿ã§ãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 16,
"tag": "p",
"text": "ååãšè¢«åã®äž¡æ¹ãšã现ããæ³åŸã®ç¥èããªããä»äºã§å¿ããã®ãæ®éãªã®ã§ãååã»è¢«åãšããããããåŒè·å£«(ã¹ããããè±:lawyer)ã代ç人ã«ããŠãŠè£å€æã§è£å€ãé²ããŠãããã®ãäžè¬çã§ãããªããåŒè·å£«ã«ãªããã®ã¯ãæ¥æ¬åœã®å Žåãåœã®è¡ãåžæ³è©Šéš(ãã»ã ããã)ã®åæ Œè
ã®ã¿ã§ããã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 17,
"tag": "p",
"text": "倿±ºã決ãã人ã¯èª°ããšãããšããã®è£å€æã®è£å€å®ã倿±ºã決ããŠããŸãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 18,
"tag": "p",
"text": "è£å€å®ã¯åå(ãããã)ãšè¢«å(ã²ãã)ã®äž¡æ¹ã®èšãåãèãã蚌æ (ãããã)ãªã©ã調ã¹ãäžã§ãæ³åŸãšãç
§ããããããŠã倿±ºã決ããŸãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 19,
"tag": "p",
"text": "æçµçã«å€æ±ºã決ããã®ã¯è£å€å®ã§ãããæ°äºè£å€ã§ã¯ããªãã¹ãåœäºè
ã©ããã話ããã£ãŠãåæºã«è§£æ±ºããããšãè£å€æã¯å§ããŠããŸãããããåœäºè
ã©ããã§è©±ãåããããŠè§£æ±ºããã°ãè£å€ãåããããããšãåºæ¥ãŸãããã®åœäºè
ã©ããã§ã®è£å€ã®è§£æ±ºãåè§£(ããã)ãšèšããŸãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 20,
"tag": "p",
"text": "ãŸããè£å€æã«ä»²è£ãç³ãåºãŠãè£å€å®ãšèª¿åå¡(ã¡ãããŠããã)ã«ãåœäºè
ã©ããã®è©±ãåãã®éã«å
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ã®åæ¹ã®çŽåŸã§ãã解決æ³ãææ¡ããŠããã調å(ã¡ãããŠã)ããããŸãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 21,
"tag": "p",
"text": "åè§£ã調åã§ããåœäºè
ãçŽåŸããªãå Žåã«ãè£å€å®ã«ããè£å€ãè¡ãããããšã«ãªããŸãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 22,
"tag": "p",
"text": "æ°äºè£å€ã§ã¯ãè£å€æã¯ãåœäºè
ã倿±ºã«åŸããªãå Žåã«ã¯ã匷å¶çã«å€æ±ºãå®è¡ããæš©éãæã€ããã®å€æ±ºãå®è¡ããããšã匷å¶å·è¡(ããããã ãã£ãã)ãšèšãããã匷å¶å·è¡ã®å¶åºŠãç¡ããšãããšãããããè£å€ãèµ·ããæå³ãç¡ããªã£ãŠããŸãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 23,
"tag": "p",
"text": "(â» ç¯å²å€: ) ãªããè£å€ã®å€æ±ºã«ããšã¥ã匷å¶å·è¡ã«ãããã£ãŠã匷å¶å·è¡ã®éªéãããããšã¯ãåäºçœ°ã®å¯Ÿè±¡ã«ãªãç¯çœªã§ããäžè¬ã«ã匷å¶å·è¡åŠšå®³çœªã(ããããããã£ãã ãŒããããã)ãªã©ãšèšããŸããäžéã«ã¯ããšãã©ãããæ°æ³ã«éãã£ãŠããèŠå¯ã«ã¯æãŸããªãã(Ã?)ãšåéãããŠãã人ãããŸããããããŸã§ãæ°æ³ã«éåããŠãèŠå¯ã«æãŸããªãã§æžãå Žåãšã¯ãæ°äºè£å€ã®å€æ±ºã«åŸã£ãŠåŒ·å¶å·è¡ãåãå
¥ããæã®å Žåã§ããåæ³ã«ã匷å¶å·è¡åŠšå®³çœªãèŠå®ãããŠããŸãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 24,
"tag": "p",
"text": "",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 25,
"tag": "p",
"text": "åäºè£å€ãšã¯ã殺人äºä»¶ã匷ç(ãããšã)ã»çªç(ãã£ãšã)ãªã©ã®ç¯çœªè¡çºãè£ãããã®è£å€ã§ãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 26,
"tag": "p",
"text": "ååã¯æ€å¯å®(ãããã€ãããè±:prosecutor ããã»ãã¥ãŒã¿)ã§ãã åäºè£å€ãèµ·ããããšã 起蚎(ãããè±:criminal charge)ãšããã èµ·èšŽã®æ±ºå®æš©ãæã£ãŠãã®ã¯ãæ€å¯ã ãã§ãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 27,
"tag": "p",
"text": "ç¯çœªãè¡ã£ãçãããããšèšŽããããåŽã®äººã 被å人(ã²ããã«ã) ãšèšããŸãã ãŸããç¯çœªããããªã£ãããããã®ãã人ã 被çè
(ã²ããã)ãšãããŸãã ã€ãŸã起蚎ããã被çè
ã被å人ã§ãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 28,
"tag": "p",
"text": "",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 29,
"tag": "p",
"text": "被çè
ãããã£ãããããæç¹ã§ã¯ããŸã ç¯äººãšã¯æ±ºãŸã£ãŠããŸããã 倿±ºã§æçœªå€æ±ºã確å®ãããŸã§ã¯ã被å人ã¯ç¡çœªãšããŠèŠãªãããããã®ããšã æšå®ç¡çœªã®åå(ãããŠãããã ã® ãããã)ãšããã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 30,
"tag": "p",
"text": "è£å€ã§ãè£å€å®ã蚌æ ãæ³åŸãªã©ãšç
§ããããããŠã被çè
ãç¯äººã§ãããã©ããã倿ããŸãã ãããŠç¯çœªã§ãã£ãå Žåã«ã¯ãè£å€å®ã¯è¢«å人ã«å眰ãèšãããããç¯çœªã§ãªãå Žåã¯ç¡çœªãèšããããã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 31,
"tag": "p",
"text": "被çè
ãæ³åŸã®ç¥èããªããŠãäžåœãªå€æ±ºãåºãããªãããããã被çè
ã¯åŒè·å£«(ã¹ããã)ãåŒè·äºº(ã¹ããã«ã)ãšããŠãã€ããããšãåºããŸãã被çè
ãè²§å°ã§åŒè·å£«ãäŸé Œã§ããªãå Žåã¯ãåœãåŒè·äººãã€ããããã®åœãã€ããåŒè·äººã®ããšãåœéžåŒè·äºº(ãããã ã¹ããã«ã)ãšããã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 32,
"tag": "p",
"text": "",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 33,
"tag": "p",
"text": "æ¥æ¬ã®å眰ã§ã¯ãæ»åããæãéãå眰ã§ãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 34,
"tag": "p",
"text": "åäºäºä»¶ã§ãèŠå¯ã鮿ãã容çè
ãæ€å¯ã«åŒãæž¡ãããšãã鿀ã(ãããã)ãšãããŸã(â» ããã€ãã®æ€å®æç§æžã®å³è¡šãªã©ã«æžããŠãã. )ã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 35,
"tag": "p",
"text": "鿀ã¯ã鮿åŸãã48æé以å
ãŸã§ã«è¡ããªããšãããŸãã(â» æž
æ°Žæžé¢ã®æ€å®æç§æžã§ç޹ä»ãããŠã. ã€ãŸãäžåŠç¯å²å
)ã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 36,
"tag": "p",
"text": "ãŸããåäºäºä»¶ã§ãåäºè£å€æã§å®éã«è£å€ãããããšããå
¬å€ã(ããã¯ã)ãšãããŸã(â» æ€å®æç§æžã®å³è¡šãªã©ã«æžããŠãã )ã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 37,
"tag": "p",
"text": "èŠå¯å®(è±èª:police officer )ã¯ãè£å€å®ã®çºè¡ãã 什ç¶(ããããããè±:warrant ã¯ãŒã¬ã³ã) ãç¡ããã°ãååãšããŠé®æãå®¶å®
æçŽ¢ãåºæ¥ãªããäŸå€ã¯çŸè¡ç¯ã®å Žåã®ã¿ã什ç¶ãç¡ããŠã鮿ã§ãã(æ²æ³ç¬¬33æ¡ãªã©ã§å®ããããŠãã)ã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 38,
"tag": "p",
"text": "èŠå¯å®ãªã©ã«ããæ·åã¯çŠæ¢ãããŠããããŸãæ·åã«ãã£ãŠåŸãããèªçœ(ãã¯ããè±:confession ã³ã³ãã§ã·ã§ã³)ã¯èšŒæ ãšããŠã¯èŠãªãããªãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 39,
"tag": "p",
"text": "ãŸãã被çè
ã»è¢«å人ã¯ãèªåã®äžå©ã«ãªãããšã¯ãããã¹ããªããŠãè¯ãæš©å©ãäžããããŠããããããé»ç§æš©(ããã²ãããè±:Right to remain silent)ãšããã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 40,
"tag": "p",
"text": "åäºè£å€ã§ã¯è¢«å人ã«å
¬éè£å€ãåããæš©å©ãèªããŠããã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 41,
"tag": "p",
"text": "ã©ã®ãããªè¡çºãç¯çœªã§ãããã¯ããããããæ³åŸã§å®ããããŠãªããã°ãªããªããããã çœªåæ³å®äž»çŸ©(ãããã ã»ããŠããã
ããè±:no penalty without a law) ãšããã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 42,
"tag": "p",
"text": "è¡çºã®ããšã«äœãããæ³åŸã§ã¯æçœªã«ããããšã¯åºæ¥ãªããè¡çºã®æç¹ã§é©æ³ã ã£ãè¡çºã¯ãæçœªã«ãããªããæ³åŸãã§ããããšã«ãå¶å®åã«ããã®ãŒã£ãŠåŠçœ°ããããšã¯çŠæ¢ããããããã é¡ååŠçœ°ã®çŠæ¢(ããã
ãããã°ã€ ã® ããã) ãšããã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 43,
"tag": "p",
"text": "æçœªã蚌æã§ãã蚌æ ãç¡ãå Žåã«ã¯ãç¡çœªãããã¯è¢«åäººã®æå©ã«ããªããã°ãªããªãããçãããã¯çœ°ããããçãããã¯è¢«å人ã®å©çã«ã(ã©ãã³èª:in dubio pro reo)",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 44,
"tag": "p",
"text": "åã調ã¹ã§ãæ·å(ãããã)ãªã©ã®ãç¡çãªåã調ã¹ããããªããããè¿å¹Žãåã調ã¹ã®ããããé²é³ã»é²ç»ããããš(å¯èŠå)ãè°è«ãããŠããŸãã",
"title": "æ°äºè£å€ãšåäºè£å€"
},
{
"paragraph_id": 45,
"tag": "p",
"text": "ãŸããæé«è£å€æã®è£å€å®ã«ã¯ãåœæ°ã®çŽæ¥æç¥šã«ããåœæ°å¯©æ»(ããã¿ã ããã)ããããããè£å€å®ã«ã¯ããµãããããªããšããåœæ°æç¥šãéåæ°ã«éãããšè£å€å®ã¯å°äœã倱ãã(æ²æ³79æ¡) åœæ°å¯©æ»ãè¡ãããææã¯ãåœæ¿ã®è¡è°é¢è°å¡ã®ç·éžæã®ãšãã«ãåæã«è¡ããããæé«è£ã®è£å€å®ã®ä»»åœåŸãã¯ãããŠã®ç·éžæã®ãšããšããã®åŸ10幎ããšã«ããã®è£å€å®ã®å¯©æ»ãè¡ãããã",
"title": "åœæ°ãšäžæš©ãšã®é¢ãã"
},
{
"paragraph_id": 46,
"tag": "p",
"text": "æ¥æ¬ã§ã¯ããã誰ããè¡æ¿æ©é¢(åœãŸãã¯å°æ¹å
Œ
±å£äœãªã©)ã®ããã§æš©å©ã䟵害ãããå Žåã«èšŽããå Žåã«ã¯ãæ°äºè£å€ãšããŠè¡æ¿æ©é¢ã被åã«ããŠèšŽããããšã«ãªãã®ã§ãããããã®ãããªè£å€ã®ããšãè¡æ¿è£å€(ããããã ããã°ã)ãšããã",
"title": "è¡æ¿è£å€"
},
{
"paragraph_id": 47,
"tag": "p",
"text": "ã€ãŸããæ°äºè£å€ã®äžã€ãšããŠãè¡æ¿è£å€ã¯æ±ãããã蚎ãã®æç¶ãã¯ãæ°äºè£å€ãšãã»ãŒåãã§ããã圢åŒçã«ã¯æ°äºè£å€ãšããŠæ±ãããã",
"title": "è¡æ¿è£å€"
},
{
"paragraph_id": 48,
"tag": "p",
"text": "ãªããå€§æ¥æ¬åžåœæ²æ³ã®æä»£ã«ã¯ãè¡æ¿è£å€æãšããç¬ç«è£å€æããã£ãããçŸåšã§ã¯ãè¡æ¿è£å€æã¯ååšããªããæ¥æ¬åœæ²æ³ã®ç¬¬67æ¡ãç¹å¥è£å€æã¯ããããèšçœ®ããããšãã§ããªãããã«ãããè¡æ¿è£å€æãšè»æ³äŒè°ã¯çŠæ¢ãããŠãããšèããããŠããã",
"title": "è¡æ¿è£å€"
},
{
"paragraph_id": 49,
"tag": "p",
"text": "ã€ãŸããç¬¬äºæ¬¡å€§æŠåŸã®æ¥æ¬ã§ã¯ã",
"title": "è¡æ¿è£å€"
},
{
"paragraph_id": 50,
"tag": "p",
"text": "ãè¡æ¿è£å€æããšãè¡æ¿è£å€ããšã¯ãç°ãªãæŠå¿µ(ãããã)ãªã®ã§ãæ··åããªãããã«ã",
"title": "è¡æ¿è£å€"
},
{
"paragraph_id": 51,
"tag": "p",
"text": "æ²æ³ãæ°æ³ãåæ³ãåæ³ãæ°äºèšŽèšæ³(ã¿ããããããã»ã)ãåäºèšŽèšæ³(ãããããããã»ã)ã®6ã€ã®æ³åŸããå
æ³ã(ãã£ãœã)ãšããã ãã®å
æ³ã¯ãä»ã®å€ãã®æ³åŸã®åºæ¬ã«ãªã£ãŠããã",
"title": "åºæ¬ãšãªãæ³åŸ"
},
{
"paragraph_id": 52,
"tag": "p",
"text": "æ°äºè£å€ã¯ãäž»ã«ãæ°æ³ãšæ°äºèšŽèšæ³ã𿲿³ã«åºã¥ããŠè¡ããããæ°äºèšŽèšæ³ã¯ãæ°äºè£å€ã§ã®æç¶ããªã©ãå®ããæ³åŸã§ããã",
"title": "åºæ¬ãšãªãæ³åŸ"
},
{
"paragraph_id": 53,
"tag": "p",
"text": "åäºè£å€ã¯ãäž»ã«åæ³ãšåäºèšŽèšæ³ã𿲿³ã«åºã¥ããŠè¡ãããã",
"title": "åºæ¬ãšãªãæ³åŸ"
},
{
"paragraph_id": 54,
"tag": "p",
"text": "2009幎(å¹³æ21幎)ãããäžè¬ã®åœæ°ã è£å€å¡(ããã°ããã) ãšããŠåžæ³ã«åå ãã è£å€å¡å¶åºŠ(ããã°ãããããã©) ãå°å
¥ããããåœæ°ãåžæ³ã«åå ãããããšã§ãåœæ°ã®åžæ³ãžã®ä¿¡é Œãé«ããã®ãå¶åºŠã®ãããã",
"title": "åžæ³å¶åºŠæ¹é©"
},
{
"paragraph_id": 55,
"tag": "p",
"text": "åäºäºä»¶ã ããè£å€å¡å¶åºŠã察象ã§ã殺人äºä»¶ã匷çãªã©ã®ãé倧ãªäºä»¶ã«ã®ã¿éããè£å€å¡ã亀ããè£å€ãè¡ãããã",
"title": "åžæ³å¶åºŠæ¹é©"
},
{
"paragraph_id": 56,
"tag": "p",
"text": "ããåŒãã§ã18æ³ä»¥äžã®åœæ°ã®6åããéžã°ããè£å€å¡(ããã°ããã)ãã¡ãã3åã®è£å€å®ãšã®ãåèš9人ã§è°è«ããªãã倿±ºã決ããã",
"title": "åžæ³å¶åºŠæ¹é©"
},
{
"paragraph_id": 57,
"tag": "p",
"text": "第äžå¯©ã®ã¿ãè£å€å¡ãåå ããäºå¯©ããã¯è£å€å®ã ãã®è£å€ã«ãªãã",
"title": "åžæ³å¶åºŠæ¹é©"
},
{
"paragraph_id": 58,
"tag": "p",
"text": "è£å€å¡ã«éžã°ããããååãšããŠèŸéã¯åºæ¥ãªãããã ããéãç
æ°ãªã©ãããå Žåã¯èŸéã§ããã",
"title": "åžæ³å¶åºŠæ¹é©"
},
{
"paragraph_id": 59,
"tag": "p",
"text": "è£å€å¡ã«ã¯ãè£å€å¡ãšããŠè·åäžã§ç¥ãåŸãç§å¯ãå®ã矩åããããç§å¯ãå€éšã«ããã¹ã£ããå
¬è¡šãããããŠã¯ãããªããå®ç§çŸ©å(ãã
ã²ãã)ãšèšãã",
"title": "åžæ³å¶åºŠæ¹é©"
},
{
"paragraph_id": 60,
"tag": "p",
"text": "å°å¹Žç¯çœªã«ã€ããŠã¯ãç¹å¥ã®é
æ
®ããªãããäžè¬ã®åäºèšŽèšãšã¯ãæç¶ããç°ãªãã ããã§èšããå°å¹Žç¯çœªãããå°å¹Žäºä»¶ãã§èšããå°å¹Žããšã¯ãæªæå¹Žã®ããšã§ãããæ§å¥ã¯ç·å¥³ãšãã«ãµããã",
"title": "å°å¹Žæ³"
},
{
"paragraph_id": 61,
"tag": "p",
"text": "åäºäžã®è²¬ä»»ã¯ã14æ³ä»¥äžã察象ã§ããã äºä»¶ãèµ·ããã人éãã20æ³æªæºã§14æ³ä»¥äžã®å ŽåãååãšããŠå®¶åºè£å€æã®å°å¹Žå¯©å€(ããããã ããã±ã)ã§ãã€ããã",
"title": "å°å¹Žæ³"
},
{
"paragraph_id": 62,
"tag": "p",
"text": "ãã®ãããªå°å¹Žã®ç¯çœªã«ã€ããŠã®è£å€ã®æç¶ããå®ããæ³åŸãå°å¹Žæ³(ãããããã»ã)ã§ããã å°å¹Žã®ç¯çœªã®å Žåã¯ãè£å€ã§ã¯ã眪ãäžããããšããããç«ã¡çŽããã£ãããäžããããšãéèŠãããã",
"title": "å°å¹Žæ³"
},
{
"paragraph_id": 63,
"tag": "p",
"text": "ãã¬ããæ°èãªã©ã§ãç¯çœªãèµ·ãããå°å¹Žã®ååãå
¬è¡šãããªãã®ã¯ãå°å¹Žæ³ã«ããé
æ
®ã«ããšã¥ãã",
"title": "å°å¹Žæ³"
},
{
"paragraph_id": 64,
"tag": "p",
"text": "眪ã®éãã«ãããä¿è·èгå¯ã»å°å¹Žé¢éèŽã»äžåŠåãªã©ã®åŠåãæ±ºããããã",
"title": "å°å¹Žæ³"
},
{
"paragraph_id": 65,
"tag": "p",
"text": "ãã ããå°å¹Žã®èµ·ãããäºä»¶ãé倧äºä»¶ã®å Žåãå°å¹Žã§ãã£ãŠãåäºè£å€ãåããå Žåããã(ãééããšãã)ã",
"title": "å°å¹Žæ³"
},
{
"paragraph_id": 66,
"tag": "p",
"text": "å°å¹Žæ³ã®ãæªæå¹Žã®ç¯çœªè
ã«ã¯å¯å®¹ãªå§¿å¢ããå°å¹Žç¯çœªãå©é·ãããŠãããšããäžè«ãããããã®ãããªäžè«ã«ããšã¥ãã2000幎(å¹³æ12幎)ã«ã¯å°å¹Žæ³ã®äžéšãå³çœ°åã®æ¹åã«æ¹æ£ãããåäºçœ°ã®é©çšå¹Žéœ¢ã16æ³ä»¥äžãã14æ³ä»¥äžãžãšåŒãäžããããã",
"title": "å°å¹Žæ³"
},
{
"paragraph_id": 67,
"tag": "p",
"text": "",
"title": "å°å¹Žæ³"
},
{
"paragraph_id": 68,
"tag": "p",
"text": "ãã容çè
ããã»ããšãã¯ç¡å®ãªã®ã«ãééã£ãææ»ããééã£ãåã調ã¹ãééã£ãéå®ãªã©ã§ãæçœªã«ãªã£ãŠããŸãããšãããã眪ã(ãããã)ãšãããŸãã(â» ããçœªã¯æŒ¢åã§ãå€çœªããšæžãã)",
"title": "ãã眪äºä»¶"
},
{
"paragraph_id": 69,
"tag": "p",
"text": "1990å¹Žã«æ æšçã®è¶³å©åžã§ãåœæ4æ³ã®å¥³å
ã®éºäœãçºèŠãããäºä»¶ã§ã容çè
ãšããŠè
å®¶å©å(ããã ãšããã)ããã鮿ãããŸãããåã調ã¹ã§ã¯ããã£ããã¯çœªãèªããŸããããè£å€ã§ã¯ç¡å®ã䞻匵ããŸãããããã倿±ºã¯ãå°å
¥åŸãŸããªãDNAéå®ã®çµæãªã©ã決ãæãšãªã£ãŠãæçœªãšãªãç¡ææ²åœ¹ãèšãæž¡ãããŸããã",
"title": "ãã眪äºä»¶"
},
{
"paragraph_id": 70,
"tag": "p",
"text": "ããããå審ãèªããè£å€ã«ãããåéå®ãèªããããææ°ã®DNAé宿è¡ã§éå®ããããšãããè
å®¶ ããã®ãã®ã§ã¯ãªãå¯èœæ§ãæ¿åã«ãªããŸããããããŠãè
å®¶ããã¯2009幎ã«éæŸãããŸãããããã«2010幎ãç¡çœªã確å®ããŸããã",
"title": "ãã眪äºä»¶"
},
{
"paragraph_id": 71,
"tag": "p",
"text": "ãªãããã®è
å®¶ããã®äžé£ã®äºä»¶ããè¶³å©äºä»¶ã(ãããã ããã)ãšãããŸã(â» æ€å®æç§æžã§ã¯ãæ°èã®ç»åãªã©ã§äºä»¶åã玹ä»ãããŠãã)ã",
"title": "ãã眪äºä»¶"
},
{
"paragraph_id": 72,
"tag": "p",
"text": "æ¥æ¬ã§ã¯ãæãéãå眰ãšããŠæ»åããããŸãããå€åœã«ã¯æ»åã廿¢ããŠããåœããããŸãã",
"title": "æ»åå¶åºŠã®è°è«"
},
{
"paragraph_id": 73,
"tag": "p",
"text": "廿¢ã®æ ¹æ ãšããŠãããèšãããŠããã®ã¯ã",
"title": "æ»åå¶åºŠã®è°è«"
},
{
"paragraph_id": 74,
"tag": "p",
"text": "ãªã©ã®äž»åŒµã§ãã",
"title": "æ»åå¶åºŠã®è°è«"
},
{
"paragraph_id": 75,
"tag": "p",
"text": "",
"title": "æ»åå¶åºŠã®è°è«"
},
{
"paragraph_id": 76,
"tag": "p",
"text": "1891幎ãæã¯ææ²»æä»£ããã·ã¢ã®ç倪åã®ãã³ã©ã€2äž(ãã·ã¢èª: ÐОкПлай II, ã©ãã³æå衚èš: Nicholai II)ãæ¥æ¬ã蚪åããæ¥æ¬æ¿åºã¯ãã³ã©ã€ãæ¥åŸ
ããŠããã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 77,
"tag": "p",
"text": "åœæã®æ¥æ¬ã¯è¿ä»£åããã°ããã®å°åœã§ããããã£ãœãããã·ã¢ã¯å€§åœã§ãã£ãã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 78,
"tag": "p",
"text": "ç倪åãã³ã©ã€ãæ»è³çã®å€§æŽ¥çº(ããã€ã¡ãããçŸåš:倧接åž)ã蚪åäžã«ãèŠåã®ä»äºã ã£ãã¯ãã®æ¥æ¬äººã®å·¡æ»ã®æŽ¥ç°äžèµ(ã€ã ãããã)ã«ãã£ãŠããã³ã©ã€ããµãŒãã«ã§åãã€ãããããšããäºä»¶ããèµ·ããã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 79,
"tag": "p",
"text": "ç¯äººã®æŽ¥ç°ã¯ããã®å Žã§åãæŒãããããæãŸã£ãã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 80,
"tag": "p",
"text": "äºä»¶ã®ãããŸãã®é倧ãã«ãææ²»å€©çãç·æ¥ã«ãã³ã©ã€ç倪åãèŠèãäºæ
ãšãªã£ãã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 81,
"tag": "p",
"text": "ãã®äºä»¶ã§ãæ¥æ¬ã®æ¿åºã¯ãã·ã¢ã®å ±åŸ©(ã»ããµã)ãããããŠãç¯äººãæ»åã«ããããã«èŠæ±ããã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 82,
"tag": "p",
"text": "ããããåœæã®æé«è£å€æã§ããã倧審é¢ã(ã ããããã)ã®é¢é·ã§ããå
å³¶æè¬(ãã㟠ãããã)ã®äž»åŒµã«ãããšãæ¥æ¬ã®(åœæã®)åæ³ã®æ³åŸã«ããšã¥ããšãçæ(ãããã)以å€ã«å¯ŸããŠã®æ®ºäººæªé(ãã€ãã ã¿ãã)ã®å Žåã¯ãæ¥æ¬ã®æ³åŸã§ã¯æ»åã«ã¯ã§ããããããã£ãŠç¡ææ²åœ¹(ãã ã¡ãããã)ããµãããããšäž»åŒµããã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 83,
"tag": "p",
"text": "ãŸããåæ³ã§ããçæãšã¯ãæ¥æ¬ã®å€©ç(ãŠãã®ã)ã»çå(ãããã)ã»ç倪å(ããããã)ãªã©ã®ããšã§ãã£ãŠãä»åœã®çæã»çæã®ããšã§ã¯ãªããšãå
å³¶ã¯äž»åŒµããã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 84,
"tag": "p",
"text": "æ¿åºã¯ããªããã ãæ³åŸããŸããã¹ããªã®ã? ãããšããã·ã¢ã«å ±åŸ©ãããªãããã«ããŠåœã®å®å
šããŸããã¹ããªã®ã?",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 85,
"tag": "p",
"text": "åœã®å®å
šã倧äºã ããããšèšã£ãŠãããæ³åŸã«ãããããã«æ»åã«ããããæ¬§ç±³ã¯ããããçç±ã«ããŠããæ¥æ¬ã¯æ³åŸãå®ããªãåœã ããšããŠãæ¬§ç±³ãæ¥æ¬ã䟵ç¥ããããã®å£å®ãããããŠããŸããããã£ãŠåœã®å®å
šããå±éº(ããã)ã«ããŠããŸãã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 86,
"tag": "p",
"text": "æ¥æ¬ã®æ¿åºã«ãšã£ãŠæ©ãŸããäºä»¶ã§ãã£ãã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 87,
"tag": "p",
"text": "æ¥æ¬ã®æ°èãªã©ã®äžè«ã¯ãããã«æ³šç®ãããæ¥æ¬ã ãã§ãªããæ¬§ç±³ãããã®äºä»¶ã®å€æ±ºã«é¢å¿ããã£ãã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 88,
"tag": "p",
"text": "çµå±ãæ¥æ¬ã®è£å€æã¯ãæ³åŸã«ãããã£ãŠã接ç°å·¡æ»ãç¡ææ²åœ¹(ãã ã¡ãããã)ã«ããããšã«æ±ºãŸã£ãã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 89,
"tag": "p",
"text": "æ¥æ¬ã®æ³åŸã«ããšã¥ãã倿±ºã¯ãåœæã®æ¬§ç±³ãããæ¥æ¬ã®è¿ä»£åã®é²å±ã¶ãã瀺ããã®ããšãããµãã«é«ãè©äŸ¡ããããã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
},
{
"paragraph_id": 90,
"tag": "p",
"text": "çŸä»£ã§ã¯ãåžæ³æš©ã®ç¬ç«ã®ã代衚çãªäºäŸãšããŠããã®å
å³¶(ãããŸ)ã®ãšã£ãè¡åãããããã€ãããŠããã",
"title": "åèïŒå€§æŽ¥äºä»¶ãšåžæ³æš©ã®ç¬ç«"
}
] | null |
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[[category:ãã³ã·ã§ã³æšæºç®¡çå§èšå¥çŽæž|09]]
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2011-10-29T04:26:17Z
|
[
"ãã³ãã¬ãŒã:Stub"
] |
https://ja.wikibooks.org/wiki/%E3%83%9E%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%B3%E6%A8%99%E6%BA%96%E7%AE%A1%E7%90%86%E5%A7%94%E8%A8%97%E5%A5%91%E7%B4%84%E6%9B%B8%E7%AC%AC9%E6%9D%A1
|
16,437 |
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(éç¥çŸ©å)
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|
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[[category:ãã³ã·ã§ã³æšæºç®¡çå§èšå¥çŽæž|12]]
| null |
2011-10-29T04:30:55Z
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[
"ãã³ãã¬ãŒã:Stub"
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https://ja.wikibooks.org/wiki/%E3%83%9E%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%B3%E6%A8%99%E6%BA%96%E7%AE%A1%E7%90%86%E5%A7%94%E8%A8%97%E5%A5%91%E7%B4%84%E6%9B%B8%E7%AC%AC12%E6%9D%A1
|
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(ä¹ã®äœ¿çšè
責任)
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[[category:ãã³ã·ã§ã³æšæºç®¡çå§èšå¥çŽæž|15]]
| null |
2011-10-29T04:34:18Z
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[
"ãã³ãã¬ãŒã:Stub"
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https://ja.wikibooks.org/wiki/%E3%83%9E%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%B3%E6%A8%99%E6%BA%96%E7%AE%A1%E7%90%86%E5%A7%94%E8%A8%97%E5%A5%91%E7%B4%84%E6%9B%B8%E7%AC%AC15%E6%9D%A1
|
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æ³åŠïŒã³ã³ã¡ã³ã¿ãŒã«ãã³ã·ã§ã³æšæºç®¡çå§èšå¥çŽæž ïŒåïŒïŒæ¬¡ïŒ
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[[category:ãã³ã·ã§ã³æšæºç®¡çå§èšå¥çŽæž|20]]
| null |
2011-10-29T04:36:10Z
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[
"ãã³ãã¬ãŒã:Stub"
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https://ja.wikibooks.org/wiki/%E3%83%9E%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%B3%E6%A8%99%E6%BA%96%E7%AE%A1%E7%90%86%E5%A7%94%E8%A8%97%E5%A5%91%E7%B4%84%E6%9B%B8%E7%AC%AC20%E6%9D%A1
|
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|
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[[category:ãã³ã·ã§ã³æšæºç®¡çå§èšå¥çŽæž|22]]
| null |
2011-10-29T04:39:24Z
|
[
"ãã³ãã¬ãŒã:Stub"
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https://ja.wikibooks.org/wiki/%E3%83%9E%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%B3%E6%A8%99%E6%BA%96%E7%AE%A1%E7%90%86%E5%A7%94%E8%A8%97%E5%A5%91%E7%B4%84%E6%9B%B8%E7%AC%AC22%E6%9D%A1
|
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[[category:ãã³ã·ã§ã³æšæºç®¡çå§èšå¥çŽæž|23]]
| null |
2011-10-29T04:42:30Z
|
[
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https://ja.wikibooks.org/wiki/%E3%83%9E%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%B3%E6%A8%99%E6%BA%96%E7%AE%A1%E7%90%86%E5%A7%94%E8%A8%97%E5%A5%91%E7%B4%84%E6%9B%B8%E7%AC%AC23%E6%9D%A1
|
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[[category:ãã³ã·ã§ã³æšæºç®¡çå§èšå¥çŽæž|24]]
| null |
2011-10-29T04:44:37Z
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https://ja.wikibooks.org/wiki/%E3%83%9E%E3%83%B3%E3%82%B7%E3%83%A7%E3%83%B3%E6%A8%99%E6%BA%96%E7%AE%A1%E7%90%86%E5%A7%94%E8%A8%97%E5%A5%91%E7%B4%84%E6%9B%B8%E7%AC%AC24%E6%9D%A1
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