[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7648#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7648","headline":"\u30af\u30e9\u30a4\u30b9\u30ea\u570f – Wikipedia","name":"\u30af\u30e9\u30a4\u30b9\u30ea\u570f – Wikipedia","description":"\u570f\u8ad6\u306b\u304a\u3044\u3066\u30af\u30e9\u30a4\u30b9\u30ea\u570f\uff08\u30af\u30e9\u30a4\u30b9\u30ea\u3051\u3093\u3001\u82f1: Kleisli category\uff09\u3068\u306f\u3001\u300e\u3059\u3079\u3066\u306e\u30b9\u30bf\u30f3\u30c0\u30fc\u30c9\u69cb\u6210\u306f\u95a2\u624b\u306e\u968f\u4f34\u5bfe\u304b\u3089\u5f97\u3089\u308c\u308b\u304b\u300f\u3068\u3044\u3046\u4e88\u60f3\u306b\u5bfe\u3057\u3001\u30cf\u30a4\u30f3\u30ea\u30c3\u30d2\u30fb\u30af\u30e9\u30a4\u30b9\u30ea\u304c\u89e3\u7b54\u3092\u3059\u308b\u306b\u3042\u305f\u3063\u3066\u5c0e\u5165\u3057\u305f\u570f\u3067\u3042\u308b[1]\u3002 \u30b9\u30bf\u30f3\u30c0\u30fc\u30c9\u69cb\u6210\uff08standard construction\uff1b\u4f59\u30e2\u30ca\u30c9\uff09\u306e\u6982\u5ff5\u306f\u30db\u30e2\u30ed\u30b8\u30fc\u4ee3\u6570\u306e\u5206\u91ce\u3067\u306f\u65e9\u304f\u304b\u3089\u73fe\u308c\u3066\u3044\u305f\u304c\u3001\u968f\u4f34\u6982\u5ff5\u306e\u767a\u898b\u306b\u4f34\u3044\u3001\u3059\u3079\u3066\u306e\u30e2\u30ca\u30c9\u306f\u95a2\u624b\u306e\u968f\u4f34\u5bfe\u304b\u3089\u5f97\u3089\u308c\u308b\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u3044\u3046\u4e88\u60f3\u304cP.J.Hilton \u305d\u306e\u4ed6\u306b\u3088\u3063\u3066\u7acb\u3066\u3089\u308c\u3066\u3044\u305f[2]\u3002\u3053\u308c\u306b\u5bfe\u3057\u4e8c\u3064\u89e3\u7b54\u304c\u5bc4\u305b\u3089\u308c\u305f\u304c\u3001\u305d\u306e\u89e3\u7b54\u8005\u306e\u4e00\u4eba\u3067\u3042\u308b\u30cf\u30a4\u30f3\u30ea\u30c3\u30d2\u30fb\u30af\u30e9\u30a4\u30b9\u30ea\u306f\u300eEvery standard construction is induced by a pair of adjoint functors(1965)\u300f\u3067\u3001 \u5b9a\u7406 \u570f L \u306b\u304a\u3051\u308b\u30b9\u30bf\u30f3\u30c0\u30fc\u30c9\u69cb\u6210","datePublished":"2022-09-12","dateModified":"2022-09-12","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/b8f58bd3b8dda2a609d711f40001ef9643d9d530","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/b8f58bd3b8dda2a609d711f40001ef9643d9d530","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7648","about":["Wiki"],"wordCount":4723,"articleBody":"\u570f\u8ad6\u306b\u304a\u3044\u3066\u30af\u30e9\u30a4\u30b9\u30ea\u570f\uff08\u30af\u30e9\u30a4\u30b9\u30ea\u3051\u3093\u3001\u82f1: Kleisli category\uff09\u3068\u306f\u3001\u300e\u3059\u3079\u3066\u306e\u30b9\u30bf\u30f3\u30c0\u30fc\u30c9\u69cb\u6210\u306f\u95a2\u624b\u306e\u968f\u4f34\u5bfe\u304b\u3089\u5f97\u3089\u308c\u308b\u304b\u300f\u3068\u3044\u3046\u4e88\u60f3\u306b\u5bfe\u3057\u3001\u30cf\u30a4\u30f3\u30ea\u30c3\u30d2\u30fb\u30af\u30e9\u30a4\u30b9\u30ea\u304c\u89e3\u7b54\u3092\u3059\u308b\u306b\u3042\u305f\u3063\u3066\u5c0e\u5165\u3057\u305f\u570f\u3067\u3042\u308b[1]\u3002\u30b9\u30bf\u30f3\u30c0\u30fc\u30c9\u69cb\u6210\uff08standard construction\uff1b\u4f59\u30e2\u30ca\u30c9\uff09\u306e\u6982\u5ff5\u306f\u30db\u30e2\u30ed\u30b8\u30fc\u4ee3\u6570\u306e\u5206\u91ce\u3067\u306f\u65e9\u304f\u304b\u3089\u73fe\u308c\u3066\u3044\u305f\u304c\u3001\u968f\u4f34\u6982\u5ff5\u306e\u767a\u898b\u306b\u4f34\u3044\u3001\u3059\u3079\u3066\u306e\u30e2\u30ca\u30c9\u306f\u95a2\u624b\u306e\u968f\u4f34\u5bfe\u304b\u3089\u5f97\u3089\u308c\u308b\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u3044\u3046\u4e88\u60f3\u304cP.J.Hilton \u305d\u306e\u4ed6\u306b\u3088\u3063\u3066\u7acb\u3066\u3089\u308c\u3066\u3044\u305f[2]\u3002\u3053\u308c\u306b\u5bfe\u3057\u4e8c\u3064\u89e3\u7b54\u304c\u5bc4\u305b\u3089\u308c\u305f\u304c\u3001\u305d\u306e\u89e3\u7b54\u8005\u306e\u4e00\u4eba\u3067\u3042\u308b\u30cf\u30a4\u30f3\u30ea\u30c3\u30d2\u30fb\u30af\u30e9\u30a4\u30b9\u30ea\u306f\u300eEvery standard construction is induced by a pair of adjoint functors(1965)\u300f\u3067\u3001\u5b9a\u7406\u570f L \u306b\u304a\u3051\u308b\u30b9\u30bf\u30f3\u30c0\u30fc\u30c9\u69cb\u6210 (C,k,p) \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001\u570f K \u304c\u5b58\u5728\u3057\u3001\u3055\u3089\u306b (C,k,p) \u3092\u5c0e\u304d\u968f\u4f34\u3092\u6210\u3059\u4e8c\u3064\u306e\u5171\u5909\u95a2\u624b F \uff1a K \u2192 L \u3068 G \uff1a L \u2192 K \u304c\u5b58\u5728\u3059\u308b\u3002\u3092\u8a3c\u660e\u3057\u3066\u89e3\u7b54\u3057\u305f\u304c\u3001\u3053\u3053\u3067\u65b0\u305f\u306b\u968f\u4f34\u5bfe (F,G) \u3092\u69cb\u6210\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u3068\u306a\u308b\u30c9\u30e1\u30a4\u30f3\u306e\u570f K \u306f\u30af\u30e9\u30a4\u30b9\u30ea\u570f\uff08Kleisli category\uff09\u3068\u547c\u3070\u308c\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u3002\u30af\u30e9\u30a4\u30b9\u30ea\u570f\u306b\u3064\u3044\u3066\u306f\u3001\u30a4\u30bf\u30ea\u30a2\u306e\u8a08\u7b97\u6a5f\u79d1\u5b66\u8005\u30a8\u30a6\u30b8\u30cb\u30aa\u30fb\u30e2\u30c3\u30b8\u306b\u3088\u308b\u8a08\u7b97\u6a5f\u79d1\u5b66\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u610f\u5473\u8ad6\u306b\u304a\u3051\u308b\u5fdc\u7528\u304c\u30e2\u30ca\u30c9\u306e\u7406\u8ad6\u3068\u3057\u3066\u5b58\u5728\u3059\u308b\u3002Table of Contents\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\uff08Kleisli triple\uff09[\u7de8\u96c6]\u30af\u30e9\u30a4\u30b9\u30ea\u570f\uff08Kleisli category\uff09[\u7de8\u96c6]\u30e2\u30ca\u30c9\u306e\u30af\u30e9\u30a4\u30b9\u30ea\u570f[\u7de8\u96c6]\u8a08\u7b97\u6a5f\u79d1\u5b66\u306b\u304a\u3051\u308b\u5fdc\u7528[\u7de8\u96c6]\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u570f\u3068\u3057\u3066\u306e\u30af\u30e9\u30a4\u30b9\u30ea\u570f\uff08Kleisli category as category of programs\uff09[\u7de8\u96c6]\u30e2\u30c3\u30b8\u306e\u539f\u7406\uff08Moggi’s principle\uff09[\u7de8\u96c6]\u30e2\u30ca\u30c9\u5247\uff08Monad laws\uff09[\u7de8\u96c6]\u30af\u30e9\u30a4\u30b9\u30ea\u570f\u3092\u306a\u3059\u8a08\u7b97\u6982\u5ff5\u306e\u4f8b[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\uff08Kleisli triple\uff09[\u7de8\u96c6]\u570f C \u4e0a\u306e\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\uff08Kleisli triple\uff09\u3068\u306f\u3001\u95a2\u624b T\u00a0: C \u2192 C\u3001\u81ea\u7136\u5909\u63db \u03b7\uff08\u03b7A\u00a0: A \u2192 T A for A \u2208 Obj(C)\uff09\u3001\u5c04 f\u00a0: A \u2192 T B \u306b\u5bfe\u3057\u3066\u5c04 f*\u00a0: T A \u2192 T B \u3092\u4e0e\u3048\u308b\u62e1\u5f35\u6f14\u7b97\u5b50\uff08extension operator\uff09 _* \u304b\u3089\u306a\u308b\u4e09\u3064\u7d44 \uff08T, \u03b7, _*\uff09\u3067\u3001\u4ee5\u4e0b\u03b7A* = 1T Af*\u30fb\u03b7A = f  \u305f\u3060\u3057\u3001f\u00a0: A \u2192 T Bg*\u30fbf* = (g*\u30fbf)* \u305f\u3060\u3057\u3001f\u00a0: A \u2192 T B \u304b\u3064 g\u00a0: B \u2192 T C  \u3092\u6e80\u305f\u3059\u3082\u306e\u3092\u8a00\u3046\u3002\u30af\u30e9\u30a4\u30b9\u30ea\u570f\uff08Kleisli category\uff09[\u7de8\u96c6]\u570f C \u4e0a\u306b\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\uff08T, \u03b7, _*\uff09\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u3068\u304d\u3001\u30af\u30e9\u30a4\u30b9\u30ea\u570f\uff08Kleisli category\uff09CT \u3068\u306f\u3001\u5bfe\u8c61\u3001\u5c04\u3001\u5c04\u306e\u5408\u6210\u898f\u5247\u3092\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u5b9a\u3081\u305f\u3082\u306e\u3092\u8a00\u3046\u3002CT \u306e\u5bfe\u8c61\u306f\u3001C \u306e\u5bfe\u8c61\u3067\u3042\u308bCT \u306b\u304a\u3044\u3066\u3001\u5bfe\u8c61 A \u304b\u3089 B \u3078\u306e\u5c04\u306e\u96c6\u307e\u308a HomCT(A,B) \u306f\u3001C \u306b\u304a\u3051\u308b\u5c04\u306e\u96c6\u307e\u308a HomC(A, T B) \u3067\u3042\u308bCT \u306b\u304a\u3044\u3066\u3001\u5c04 f \u2208 HomCT(A,B) \u3068\u5c04 g \u2208 HomCT(B,C)  \u306e\u5408\u6210\u5c04\u3068\u306f\u3001g*\u30fbf\u00a0: A \u2192 T C \u3067\u3042\u308b\u30e2\u30ca\u30c9\u306e\u30af\u30e9\u30a4\u30b9\u30ea\u570f[\u7de8\u96c6]\u570f C \u4e0a\u306e\u30e2\u30ca\u30c9  \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u3059\u308b\u3068\u3001\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\u306e\u62e1\u5f35\u6f14\u7b97\u5b50 _*\u306f\u30e2\u30ca\u30c9\u3092\u7528\u3044\u3066\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u4efb\u610f\u306e\u5c04 f\u00a0: X \u2192 T Y \u306b\u5bfe\u3057\u3066\u3001_* \u3092  f\u2217=\u03bcY\u2218Tf.{displaystyle f^{*}=mu _{Y}circ Tf.}\u3068\u3059\u308b\u3002\u3088\u3063\u3066\u3001\u30e2\u30ca\u30c9  \u3092\u4e0e\u3048\u308b\u3053\u3068\u306f\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb \uff08T,\u03b7, _*\uff09 \u3092\u4e0e\u3048\u308b\u3053\u3068\u3068\u540c\u5024\u3067\u3042\u308b\u3002\u8a08\u7b97\u6a5f\u79d1\u5b66\u306b\u304a\u3051\u308b\u5fdc\u7528[\u7de8\u96c6]\u8a08\u7b97\u6a5f\u79d1\u5b66\u8005\u306e\u30a8\u30a6\u30b8\u30cb\u30aa\u30fb\u30e2\u30c3\u30b8\u306f\u3001\u30af\u30e9\u30a4\u30b9\u30ea\u570f\u306e\u5c04\u3092\u30d7\u30ed\u30b0\u30e9\u30e0\uff08program\uff09\u306b\u5bfe\u5fdc\u3055\u305b\u308b[3]\u3001\u3059\u306a\u308f\u3061\u5c04\u3068\u3057\u3066\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u6210\u3059\u570f\u3068\u306f\u30af\u30e9\u30a4\u30b9\u30ea\u570f\u3067\u3042\u308b\u3068\u3059\u308b\u3053\u3068\u3067\u8868\u793a\u7684\u610f\u5473\u8ad6\u306b\u30e2\u30b8\u30e5\u30fc\u30eb\u6027\u3092\u6301\u305f\u305b\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u305f\uff08\u30e2\u30ca\u30c9\u306e\u7406\u8ad6\uff09[4]\u3002\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u570f\u3068\u3057\u3066\u306e\u30af\u30e9\u30a4\u30b9\u30ea\u570f\uff08Kleisli category as category of programs\uff09[\u7de8\u96c6]\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u6559\u5247\u3068\u3057\u3066\u3001\u5f15\u6570\u3068\u8fd4\u308a\u5024\u3092\u3082\u3064\u3053\u3068\u304b\u3089\u30d7\u30ed\u30b0\u30e9\u30e0\uff08program\uff09\u3068\u306f\u6570\u5b66\u306e\u95a2\u6570\u3001\u3059\u306a\u308f\u3061\u96c6\u5408\u5199\u50cf\uff08mapping\uff09\u3067\u3042\u308b\u3068\u6559\u3048\u3089\u308c\u308b\u3053\u3068\u304c\u3042\u308b\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3053\u306e\u55a9\u3048\u306f\u5165\u51fa\u529b\u7b49\u3092\u3082\u305f\u3089\u3059\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b\u5916\u3092\u8fd4\u3059\u30d7\u30ed\u30b0\u30e9\u30e0\u5f15\u6570\u306b\u5bfe\u3057\u3066\u5024\u3092\u8fd4\u3055\u306a\u3044\uff08\u505c\u6b62\u3057\u306a\u3044\uff09\u30d7\u30ed\u30b0\u30e9\u30e0\u540c\u3058\u5f15\u6570\u3067\u3082\u8fd4\u308a\u5024\u304c\u7570\u306a\u308b\u53ef\u80fd\u6027\u306e\u3042\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u306a\u3069\u3092\u8aac\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u3002\u3064\u307e\u308a\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u96c6\u5408\u5199\u50cf\u3067\u306f\u306a\u3044\uff08a program is NOT a mapping\uff09[5]\u3002\u30d7\u30ed\u30b0\u30e9\u30e0\uff08program\uff09\u306e\u6570\u5b66\u7684\u30e2\u30c7\u30eb\u3092\u898b\u3064\u3051\u51fa\u3059\u904e\u7a0b\u306b\u304a\u3044\u3066\u3001\u30e2\u30c3\u30b8\u306f\u570f\u8ad6\u3068\u8868\u793a\u7684\u610f\u5473\u8ad6\u306e\u89b3\u70b9\u304b\u3089\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u570f\u306e\u5c04\u3001\u578b\u306f\u570f\u306e\u5bfe\u8c61\u3068\u307f\u306a\u3059\u3053\u3068\u304c\u3067\u304d[6]\u3001\u3055\u3089\u306b\u76f4\u611f\u7684\u89e3\u91c8\u3068\u3057\u3066\u3001\u95a2\u6570\u304c\u5024\u3092\u53d6\u308a\u5024\u3092\u8fd4\u3059\u3082\u306e\u3067\u3042\u308b\u306e\u306b\u5bfe\u3057\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u5024\u3092\u53d6\u308a\u8a08\u7b97\u3057\u305f \u5024\u3092\u8fd4\u3059[7][8]\u3001\u3059\u306a\u308f\u3061\u5f15\u6570\u306e\u578b\u3068\u8fd4\u308a\u5024\u306e\u578b\u306e\u9593\u306b\u306f\u306a\u306b\u304b\u9055\u3044\u304c\u3042\u308a\u5358\u7d14\u306a\u5c04\u306e\u5408\u6210\u304c\u3067\u304d\u306a\u3044\u3001\u3068\u8003\u3048\u305f\u3002  \u96c6\u5408\u5199\u50cf\uff08\u95a2\u6570\uff09\uff1a\u5024\u3000\u2192\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u5024\u30d7\u30ed\u30b0\u30e9\u30e0\u3000\u3000\u3000\uff1a\u5024\u3000\u2192\u3000”\u8a08\u7b97\u3057\u305f”\u3000\u5024\u30e2\u30c3\u30b8\u306f\u3053\u306e\u3088\u3046\u306a\u5c04\u3068\u3057\u3066\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u6570\u5b66\u7684\u30e2\u30c7\u30eb\u3068\u3057\u3066\u30af\u30e9\u30a4\u30b9\u30ea\u570f\uff08Kleisli category\uff09\u306e\u5c04\u304c\u59a5\u5f53\u3067\u3042\u308b\u3068\u4e3b\u5f35\u3057[9]\u5b9f\u969b\u306b\u526f\u4f5c\u7528\u3001\u4f8b\u5916\u51e6\u7406\u3001\u975e\u6c7a\u5b9a\u8a08\u7b97\u306a\u3069\u306e\u52b9\u679c[10]\u3092\u3046\u307e\u304f\u30af\u30e9\u30a4\u30b9\u30ea\u570f\u306e\u67a0\u7d44\u307f\u3067\u7d71\u4e00\u7684\u306b\u5b9a\u5f0f\u5316\u3067\u304d\u308b\u3053\u3068\u3092\u793a\u3057\u305f\u3002\u305d\u306e\u7d50\u679c\u3068\u3057\u3066\u4f1d\u7d71\u7684\u306a\u8868\u793a\u7684\u610f\u5473\u8ad6\u306b\u304a\u3044\u3066\u306f\u6b20\u5982\u3057\u3066\u3044\u305f\u30e2\u30b8\u30e5\u30fc\u30eb\u6027\u3092\u4ed8\u4e0e\u3059\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u305f[11]\u3002\u30e2\u30c3\u30b8\u306e\u539f\u7406\uff08Moggi’s principle\uff09[\u7de8\u96c6]\u7406\u8ad6\u7684\u306b\u306f\u3001\u3042\u308b\u8a08\u7b97\u65b9\u5f0f\u3067”\u8a08\u7b97\u3057\u305f”\u3053\u3068\u3092\u793a\u3059\u5370\u306f\u3001\u6b21\u306e\u30e2\u30c3\u30b8\u306e\u539f\u7406\u304b\u3089\u578b\u69cb\u7bc9\u5b50\u3068\u3057\u3066\u5c0e\u5165\u3055\u308c\u308b[12]\u3002\u30e2\u30c3\u30b8\u306e\u539f\u7406\uff08Moggi’s principle\uff09[13][14]\u8a08\u7b97\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u305f\u578b A \u306e\u5024\uff08computations of type A\uff09\u306f\u3001\u578b T A \u306e\u5024\u306b\u5bfe\u5fdc\u3059\u308b\uff08Computations of type A correspond to values of type T A.\uff09\u7279\u306b\u3001\u3053\u306e\u8a08\u7b97\u65b9\u5f0f\u3092\u8868\u3059\u578b\u69cb\u7bc9\u5b50 T \u3092\u8a08\u7b97\u6982\u5ff5\uff08a notion of computation\uff09\u3068\u547c\u3076[15]\u3002\u307e\u305f\u3001\u5fc5\u7136\u7684\u306b\u8a08\u7b97\u3057\u305f\u5024\u3092\u8fd4\u3059\u30d7\u30ed\u30b0\u30e9\u30e0\u6982\u5ff5\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002\u30e2\u30c3\u30b8\u304c\uff08\u6697\u9ed9\u7684\u306b\uff09\u4e3b\u5f35\u3059\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u6982\u5ff5\u578b A \u306e\u5f15\u6570\u3092\u53d6\u308a T \u306e\u8a08\u7b97\u52b9\u679c\u3092\u4f34\u3044\u3064\u3064\u8a08\u7b97\u3092\u3057\u305f\u578b B \u306e\u5024\u3092\u8fd4\u3059\u30d7\u30ed\u30b0\u30e9\u30e0\uff08program\uff09\u3068\u306f\u3001A \u2192 T B\u306e\u578b\u3092\u6301\u3064\u3082\u306e\u3067\u3042\u308b\u3002\u3053\u306e\u7279\u5fb4\u4ed8\u3051\u306b\u3088\u3063\u3066\u3001\u8a08\u7b97\u52b9\u679c T \u3092\u4f34\u3046\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u306a\u3093\u3089\u8a08\u7b97\u52b9\u679c\u3092\u6301\u305f\u306a\u3044\u5358\u306a\u308b\u96c6\u5408\u5199\u50cf\uff08\u95a2\u6570\uff09\u306f\u533a\u5225\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3002\u305f\u3060\u3057\u3001\u305d\u306e\u4ee3\u308f\u308a\u306b\uff12\u3064\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5408\u6210\u3092\u95a2\u6570\u306e\u3088\u3046\u306b\u5358\u7d14\u306b\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u306a\u304f\u306a\u308b\u306e\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001program1\u00a0:: A \u2192 T B \u3068 program2\u00a0:: B \u2192 T C \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u305d\u306e\u5408\u6210\u3092\u884c\u304a\u3046\u3068\u601d\u3063\u3066\u3082\u3001\u578b B \u3068\u3044\u3046\u30c7\u30fc\u30bf\u306e\u578b\u3068\u3057\u3066\u306e\u5171\u901a\u6027\u306f\u3042\u3063\u3066\u3082\u8a08\u7b97\u6982\u5ff5\u306e\u5206\u3060\u3051\u578b\u306b\u9055\u3044\u304c\u3042\u308b\u305f\u3081\u3001\u5b9f\u969b\u306b\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5408\u6210\u3092\u884c\u3046\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002program2\u00a0:: B \u2192 T C \u00d7 program1\u00a0:: A \u2192 T B \uff08\u5408\u6210\u4e0d\u53ef\uff09\u3053\u306e\u81f4\u547d\u7684\u306a\u554f\u984c\u70b9\u3092\u89e3\u6d88\u3059\u308b\u305f\u3081\u306b\u5c0e\u5165\u3055\u308c\u308b\u306e\u304c\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\uff08Kleisli triple\uff09\u3067\u3042\u308b\u3002\u76f4\u611f\u7684\u306a\u8a18\u6cd5\u3068\u306a\u308b\u304c\u3001\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\uff08T,\u03b7, _*\uff09\u304c\u4e0e\u3048\u3089\u308c\u308c\u3070\u3001\u300c_*\u300d\u6f14\u7b97\u5b50\u306e\u6a5f\u80fd\u304b\u3089program2*\u00a0:: T B \u2192 T C \u3068\u306a\u308aprogram2* . program1\u00a0:: A \u2192 T C \uff08\u5408\u6210\u53ef\u80fd\uff09\u3068\u3044\u3046\u5f62\u3067\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5408\u6210\u304c\u53ef\u80fd\u3068\u306a\u308b\u3002\u304a\u304a\u3088\u305d\u3053\u306e\u3088\u3046\u306a\u7406\u7531\u304b\u3089\u30e2\u30c3\u30b8\u306f\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u30af\u30e9\u30a4\u30b9\u30ea\u570f\u3092\u306a\u3059\u3068\u3057\u305f[16]\u3002\u30e2\u30ca\u30c9\u5247\uff08Monad laws\uff09[\u7de8\u96c6]\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u4e16\u754c\u306b\u304a\u3051\u308b\u30af\u30e9\u30a4\u30b9\u30ea\u30fb\u30c8\u30ea\u30d7\u30eb\u306b\u5bfe\u5fdc\u3059\u308b\u3082\u306e\u306f\u3001\u8a08\u7b97\u6a5f\u79d1\u5b66\u8005\u306ePhillip Wadler\u306b\u3088\u3063\u3066\u547d\u540d\u3055\u308c\u305f\u6b21\u306e\u30e2\u30ca\u30c9\u5247\uff08Monad laws\uff09\u3067\u3042\u308b\u3002{-                     \u30e2\u30ca\u30c9\u5247\uff08Monad laws\uff09                     -}{-  1.\u53f3\u5358\u4f4d\u5247\uff08Right unit\uff09\u3000-}  T a `bindT` unitT == T a{- 2.\u5de6\u5358\u4f4d\u5247\uff08Left unit\uff09\u3000 -}  (unitT a) `bindT` f == f{- 3.\u7d50\u5408\u898f\u5247\uff08Associative\uff09-}  T a `bindT` ( x \u2192 (f x) `bindT` ( y \u2192 g y) ) == (T a `bindT` (x \u2192 f x) ) `bindT` (y \u2192 g y)\u3053\u308c\u306b\u76f4\u63a5\u5bfe\u5fdc\u3059\u308b\u306e\u306f\u6b21\u306e\u5408\u6210\u9806\u5e8f\u3092\u9006\u306b\u3057\u305f\u306e\u3068\u304d\u306e\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\u3067\u3042\u308b\u3002\u5408\u6210\u9806\u5e8f\u304c\u9006\u306e\u3068\u304d\u306e\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\u570f C \u4e0a\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u624b T\u3001\u81ea\u7136\u5909\u63db \u03b7\u3001T \u3078\u306e\u5c04\u306b\u5bfe\u3059\u308b\u64cd\u4f5c _* \u304c\u4ee5\u4e0bT A\u00a0; \u03b7A*\uff1d T A\uff08\u30e2\u30ca\u30c9\u5247\u3068\u306e\u660e\u767d\u306a\u5bfe\u5fdc\u95a2\u4fc2\u3092\u3064\u3051\u308b\u305f\u3081\u3001\u5143\u3005\u306e\u5b9a\u7fa9\u3088\u308a\u3082\u5197\u9577\u306b\u3057\u3066\u3042\u308b\u3002\uff09\u03b7A\u00a0; f* \uff1d f  \u305f\u3060\u3057\u3001f\u00a0: A \u2192 T Bf*\u00a0; g* \uff1d (f\u00a0; g*)* \u305f\u3060\u3057\u3001f\u00a0: A \u2192 T B \u304b\u3064 g\u00a0: B \u2192 T C\u3092\u6e80\u305f\u3059\u3068\u304d\u3001\u4e09\u3064\u7d44\uff08T, \u03b7, _*\uff09\u3092\u30af\u30e9\u30a4\u30b9\u30ea\u30c8\u30ea\u30d7\u30eb\u3068\u547c\u3076\u3002\u30af\u30e9\u30a4\u30b9\u30ea\u570f\u3092\u306a\u3059\u8a08\u7b97\u6982\u5ff5\u306e\u4f8b[\u7de8\u96c6]\u30af\u30e9\u30a4\u30b9\u30ea\u570f\u3092\u306a\u3059\u8a08\u7b97\u6982\u5ff5\u3068\u3057\u3066\u306f\u4ee5\u4e0b\u306e\u8a08\u7b97\u52b9\u679c\u304c\u6319\u3052\u3089\u308c\u308b[17]\u3002\u90e8\u5206\u6027\uff08partiality\uff09T A = A\u22a5\uff08= A + { \u22a5 }\uff09\u03b7A \u306f A \u304b\u3089 A\u22a5 \u306e\u4e2d\u3078\u306e\u5305\u542b\uff08inclusion\uff09f\u00a0: A -> T B \u3067\u3042\u308c\u3070\u3001f*(\u22a5) = \u22a5 \u3001f*(a) = f(a) \u305f\u3060\u3057\u3001a \u2208 A\u975e\u6c7a\u5b9a\u6027\uff08nondeterminism\uff09[18]T A = Pfin(A)\u03b7A \u306f\u5358\u8981\u7d20\uff08singleton\uff09\u5199\u50cf a \u21a6 {a}f\u00a0: A -> T B \u304b\u3064 c \u2208 T A \u3067\u3042\u308c\u3070\u3001f*(c) = \u222ax \u2208 cf(x)\u526f\u4f5c\u7528\uff08side-effects\uff09T A = (A \u00d7 S)S\u03b7A \u306f\u5199\u50cf a  \u21a6 (\u03bbs: S.)f\u00a0: A -> T B \u304b\u3064 c \u2208 T A \u3067\u3042\u308c\u3070\u3001\u03bbs:S.(let "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/7648#breadcrumbitem","name":"\u30af\u30e9\u30a4\u30b9\u30ea\u570f – 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