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Categoryã«é–¢ã™ã‚‹notaeã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯ (31)

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Haskellã¨ä½™ä»£æ•°(Coalgebra) - æœæ—¥ãƒãƒƒãƒˆã€€æŠ€è¡“è€…ãƒ–ãƒã‚°
ã“ã“ã§ã¯Haskellã®ä¸ç´šè€…å‘ã‘ã®ãƒˆãƒ”ãƒƒã‚¯ã‚’ç°¡å˜ã«å–ã‚Šä¸Šã’ãŸã„ã¨æ€ã„ã¾ã™ã€‚ ä»Šå›žã¯ä½™ä»£æ•°(Coalgebra)ã«ã¤ã„ã¦ã§ã™ã€‚Haskellã‚’æ›¸ã„ã¦ã„ã‚‹ã¨ã€Žä½™ï¼ˆãªã‚“ã¨ã‹ï¼‰ã€ã¨ã„ã†è¨€è‘‰ã‚’ã¿ã‹ã‘ã‚‹ã“ã¨ãŒã‚ã‚Šã¾ã™ã€‚ã“ã‚Œã¯è‹±èªžã®æŽ¥é è¾ž Co- ã®è¨³ã§ã€ã“ã“ã§ã¯ä»£æ•°(Algebra)ã®åŒå¯¾(Dual)ã¨ã„ã†æ„å‘³ã§ä½™ä»£æ•°ã¨å‘¼ã°ã‚Œã¦ã„ã¾ã™ã€‚ ã•ã¦Haskellã‚„OCamlã®ãƒ‡ãƒ¼ã‚¿åž‹ã¯ä¸€èˆ¬ã«ä»£æ•°çš„ãƒ‡ãƒ¼ã‚¿åž‹(Algebraic data type)ã¨å‘¼ã°ã‚Œã¾ã™ã€‚ã“ã®ãƒ‡ãƒ¼ã‚¿åž‹ã«ãƒ‘ã‚¿ãƒ¼ãƒ³ãƒžãƒƒãƒãƒ³ã‚°ã‚’åŠ ãˆã¦ã€ï¼ˆã‚ªãƒ–ã‚¸ã‚§ã‚¯ãƒˆæŒ‡å‘è¨€èªžãªã©ã¨æ¯”è¼ƒã—ãŸã¨ãã®ï¼‰é–¢æ•°åž‹è¨€èªžã®ç‰¹å¾´ã¨ç´¹ä»‹ã•ã‚Œã‚‹ã“ã¨ã‚‚å¤šã„ã¨æ€ã„ã¾ã™ã€‚å®Ÿã¯ã“ã®ãƒ‡ãƒ¼ã‚¿åž‹ã«ã¯ã‚‚ã¨ã‚‚ã¨ä½™ãƒ‡ãƒ¼ã‚¿(Codata)ã¨å‘¼ã°ã‚Œã‚‹ã‚ˆã†ãªç›¸æ–¹ãŒã„ãŸã®ã§ã™ãŒã€äººé¡žãŒæ‰±ã†ã«ã¯æ—©ã™ãŽãŸã®ã‹ã€ãƒ‡ãƒ¼ã‚¿åž‹ã«æ¯”ã¹ã‚‹ã¨ä½™ãƒ‡ãƒ¼ã‚¿ã¯é•·ã‚‰ãå½±ã®å˜åœ¨ã§ã‚ã‚Šã¾ã—ãŸï¼ˆã¡ãªã¿ã«ä½™ãƒ‡ãƒ¼ã‚¿ã¯å£èªžä¸Šã¯ã‚³ãƒ‡ãƒ¼ã‚¿ã¨å‘¼ã¶ã‹ã‚‚
notae 2022/05/06
Haskell

Category
ãƒªãƒ³ã‚¯
ã‚¢ãƒ—ãƒªã‚«ãƒ†ã‚£ãƒ–é–¢æ‰‹ã£ã¦ãªã«ï¼Ÿãƒ¢ãƒŽã‚¤ãƒ‰åœã¨ã®é–¢ä¿‚ã¯ï¼Ÿèª¿ã¹ã¦ã¿ã¾ã—ãŸï¼ | é›‘è¨˜å¸³
ã“ã®è¨˜äº‹ã¯ Category Theory Advent Calendar 2018 7æ—¥ç›® ã‹ã¤ Haskell (ãã®2) Advent Calendar 2018 7æ—¥ç›®ã®è¨˜äº‹ã§ã™ã€‚ Category Theory Advent Calendar 2018ã®6æ—¥ç›®ã¯corollary2525ã•ã‚“ã®ã€Œéšä¼´ã¯ã€€ã‚ã‚‰ã‚†ã‚‹ã¨ã“ã‚ã«ã€€ç¾ã‚Œã‚‹ã€ã€8æ—¥ç›®ã¯ç©ºå¸ã€9æ—¥ç›®ã¯t_uemura669101ã•ã‚“ã®ã€Œãƒˆãƒã‚¹ã¨é«˜éšŽè«–ç†ã€ã§ã™ã€‚ Haskell (ãã®2) Advent Calendar 2018ã®6æ—¥ç›®ã¯ç©ºå¸ã€8æ—¥ç›®ã¯takoeight0821ã•ã‚“ã®ã€ŒType defaultingã«ã¤ã„ã¦ã®åˆç´šçš„ãªè§£èª¬ã€ã§ã™ã€‚ ã“ã®è¨˜äº‹ã¯ã©ã†ã„ã†è¨˜äº‹ã‹ åœè«–ã®æ–¹ã‹ã‚‰æ¥ãŸäººå‘ã‘ï¼š ãƒ‡ã‚«ãƒ«ãƒˆç©ã‚„ãƒ†ãƒ³ã‚½ãƒ«ç©ã®ä¸€èˆ¬åŒ–ã§ã‚ã‚‹ã€Œãƒ¢ãƒŽã‚¤ãƒ‰ç©ã€ã®è©±ã¨ã€ã€Œå†…éƒ¨ãƒ›ãƒ ã€ã®è©±ã‚’ã—ã¾ã™ã€‚æ–‡çŒ®ã«ã‚ˆã£ã¦ã¯å†…éƒ¨ãƒ›ãƒ ã¯ãƒ¢ãƒŽã‚¤ãƒ‰ç©ã®å³éšä¼´ã¨ã—ã¦å°Ž
notae 2019/07/19
Haskell

Category
ãƒªãƒ³ã‚¯
åœè«–ã®éšä¼´ã‚’ã¡ã‚ƒã‚“ã¨æŠ‘ãˆã‚ˆã†ï¼š ãŠçµµæãå®Œå…¨è§£èª¬ - æªœå±±æ£å¹¸ã®ã‚ãƒžã‚¤ãƒ©é£¼è‚²è¨˜ (ã¯ã¦ãªBlog)
[è¿½è¨˜ date="å¾Œæ—¥"]æ—¥æœ¬èªžã®è¡¨è¨˜ã¨ã—ã¦ã€ŒæŠ‘ãˆã‚‹ã€ã‚ˆã‚Šã€ŒæŠ¼ã•ãˆã‚‹ã€ãŒæ£ã—ã„æ°—ãŒã—ã¦ããŸã‘ã©ã€ã“ã®ã¾ã¾ã«ã—ã¾ã™ã€‚ä½¿ã„åˆ†ã‘ãŒã•ã»ã©æ˜Žç¢ºãªã‚ã‘ã˜ã‚ƒãªã„ã—ã€ã€ŒæŠ‘ãˆã‚‹ã€ã«ã€Œæ”¯é…ä¸‹ã«ç½®ãã€ã‚ˆã†ãªé›°å›²æ°—ã‚‚ã‚ã‚‹ã®ã§ã€‚[/è¿½è¨˜] ã€Œåœè«–ã®éšä¼´ã‚’ã¡ã‚ƒã‚“ã¨æŠ‘ãˆã‚ˆã†ã€ã®ãªã‹ã§ã€çµµã‚’ä½¿ã£ãŸè¨ˆç®—ã«ã¤ã„ã¦è¨€åŠã—ã¦ã„ã¾ã™ã€‚ å˜ä½ï¼ä½™å˜ä½ã¨ãƒ‹ãƒ§ãƒãƒ‹ãƒ§ãƒé–¢ä¿‚å¼ã‚’çµµï¼ˆã‚¹ãƒˆãƒªãƒ³ã‚°å›³ï¼‰ã§æã‘ã°æ¬¡ã®ã‚ˆã†ã§ã™ã€‚ ã“ã‚Œã‚‰ã®å…¬å¼ã¯ã€çµµï¼ˆã‚¹ãƒˆãƒªãƒ³ã‚°å›³ï¼‰ã‚’ä½¿ã†ã¨è‡ªç„¶ã«è§£é‡ˆã§ãã¾ã™ãŒã€ãã®è©±ã¯æ¬¡ã®æ©Ÿä¼šã«ã—ã¾ã™ã€‚ çµµï¼ˆã‚¹ãƒˆãƒªãƒ³ã‚°å›³ï¼‰ã§è¨ˆç®—ã™ã‚Œã°æ¥½ã§ã™ã€‚çµµç®—ï¼ˆpictorial/graphical/diagrammatic calculationï¼‰ã®è©±ã¯ã„ãšã‚Œã¾ã¨ã‚ã¦ã™ã‚‹äºˆå®šã§ã™ï¼ˆä»Šæ—¥ã¯ã—ãªã„ï¼‰ã€‚ çµµãŒæã‘ã‚‹ã®ã§ã€éšä¼´ç³»ã®è¨ˆç®—ã¯çµµç®—ï¼ˆpictorial/graphical/diagrammatic calculationï¼‰ã«æŒã¡è¾¼ã‚ã¾ã™ã€‚ ãƒ‹
notae 2018/04/05
Category

Math
ãƒªãƒ³ã‚¯
Contravariant ãªã‚“ã¦è¦ã‚‰ã‚“ã‹ã£ãŸã‚“ã‚„! - Qiita
Deleted articles cannot be recovered. Draft of this article would be also deleted. Are you sure you want to delete this article? -- æ¨™æº–ã® Data.Functor.Functor ã§ã¯åå¤‰é–¢æ‰‹ã‚’åŒ…æ‹¬ã§ããªã„ã®ã§ Contravariant ã¨ã„ -- ã†åˆ¥ã®ç¨®é¡žã®é–¢æ‰‹ãŒå®šç¾©ã•ã‚Œã¦ã‚‹ã€‚ã§ã‚‚æœ¬å½“ã¯ãã‚“ãªä½™åˆ†ãªå®šç¾©ã¯è¦ã‚‰ãªã„ã‚“ã ã€‚ -- å…¨éƒ¨ Functor ã«ä¸€å…ƒåŒ–ã§ãã‚‹ã€‚ãã†ã€Control.Category ãªã‚‰ãã€‚ {-# LANGUAGE MultiParamTypeClasses, TypeOperators, TypeSynonymInstances, InstanceSigs, FlexibleInstances, ScopedTypeVariab
notae 2017/11/14
Haskell

Category
ãƒªãƒ³ã‚¯
https://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf
notae 2016/11/01
Category
ãƒªãƒ³ã‚¯
ãƒ¢ãƒŠãƒ‰ãƒ¢ãƒŠãƒ‰ (LTæ²¡ãƒã‚¿) - Qiita
æ•°å¦ã‚«ãƒ•ã‚§ã®LTã§è©±ã™äºˆå®šã§ã—ãŸãŒã€ä½¿ã†æ©Ÿä¼šãŒãªããªã£ãŸã®ã§å…¬é–‹ã—ã¾ã™ã€‚ Haskellã«ãŠã‘ã‚‹ãƒ¢ãƒŠãƒ‰ã¨ã¯ Haskellã§ã¯Monadã¨ã„ã†åž‹ã‚¯ãƒ©ã‚¹ã§ãƒ¢ãƒŠãƒ‰ã‚’è¡¨ç¾ã—ã¦ã„ã¾ã™ã€‚ã“ã®åž‹ã‚¯ãƒ©ã‚¹ã¯ return :: a -> m a ã€ join :: m (m a) -> m aã€€ã€ãã—ã¦ fmap ã«ãŠã„ã¦ãƒ¢ãƒŠãƒ‰ãŒè¡¨ç¾ã•ã‚Œã¦ã„ã¾ã™ã€‚è‰²ã‚“ãªäººãŒè‰²ã‚“ãªå ´ã§èª¬æ˜Žã—ã¦ã„ã‚‹ã“ã¨ã§ã™ã‹ã‚‰ã€ä»Šã•ã‚‰ã“ã“ã§è°è«–ã‚’æŽ˜ã‚Šè¿”ã™å¿…è¦ã¯ãªã„ã§ã—ã‚‡ã†ã€‚ ãƒ¢ãƒŠãƒ‰ã«ã¯ []ã€Maybeã€State sã€Cont rã€Reader rã€Writer wã€IOã€ãªã©ãŒã‚ã‚Šã¾ã™ã€‚ã—ã‹ã—ã€ã¿ãªã•ã‚“ã¯ãã‚Œã§æº€è¶³ã§ã—ã‚‡ã†ã‹ï¼Ÿ ãã‚“ãªãƒ¢ãƒŠãƒ‰ã§å¤§ä¸ˆå¤«ã§ã™ã‹ï¼Ÿ Haskellã§ã‚‚ã£ã¨ãƒ¢ãƒŠãƒ‰ ãƒ¢ãƒŠãƒ‰ã‚’ã•ã‚‰ã«ã“ã˜ã‚‰ã›ãŸäººã¯ã€ Free ãƒ¢ãƒŠãƒ‰ã‚„ Codensity ãƒ¢ãƒŠãƒ‰ãªã©ã«æ‰‹ã‚’å‡ºã™ã§ã—ã‚‡ã†ã€‚ã“ã‚Œã‚‰ã¯å¤§å¤‰ä¾¿åˆ©ãªã‚‚ã®ã§ã™ãŒã€ãã®çã—ã•æ•…ã“ã‚Œã¾ãŸ
notae 2016/09/25
Haskell

Category

Monad
ãƒªãƒ³ã‚¯
Index of /course/80-413-713/notes
Index of /course/80-413-713/notes NameLast modifiedSizeDescription Parent Directory Â - CT2errata2010.pdf 2015-04-02 09:57 35K cats.pdf 2015-04-02 09:57 85K chap01.pdf 2015-04-02 09:57 190K chap02.pdf 2015-04-02 09:57 185K chap03.pdf 2015-04-02 09:57 179K chap04.pdf 2015-04-02 09:57 140K chap05.pdf 2015-04-02 09:57 201K chap06.pdf 2015-04-02 09:57 208K chap07.pdf 2015-04-02 09:57 242K chap08.pdf 2
notae 2016/04/12
Category
ãƒªãƒ³ã‚¯
Representable functors in Haskell
Representable functors A functor1 $F : C \to Set$ is called representable if it is isomorphic to $Hom(A, -)$ for some $A$ (denoted as $F \simeq Hom(A,-)$). Since we are talking about Haskell, Iâ€™ll also use the $(a \to -)$ notation instead of $Hom(a, -)$. The object $A$ is called representing object for a functor $F$. Usually, the isomorphism between the functor is given by two natu
notae 2016/04/11
Haskell

Category
ãƒªãƒ³ã‚¯
åœè«–ã«æœ€çŸã§å…¥é–€ã™ã‚‹ - ä¿ºã® Colimit ã‚’è¶Šãˆã¦ã‚†ã‘
ã¯ã˜ã‚ã« å¯¾è±¡èªè€… æ•°å¦ä»¥å‰ æ•°å¦ã®åŸºç¤Ž ãƒ›ãƒ¢ãƒã‚¸ãƒ¼ä»£æ•° åœè«– ã‚‚ã£ã¨æ‰‹å–ã‚Šæ—©ãåœè«–ã®å‹‰å¼·ã‚’å§‹ã‚ãŸã„äººã¸ ãŠã‚ã‚Šã« ç´¹ä»‹ã—ãŸæ›¸ç± ã¯ã˜ã‚ã« ç§ãŒåœè«–ã¨ã„ã†åˆ†é‡Žã‚’çŸ¥ã‚‹ãã£ã‹ã‘ã¯ã€ãŠãã‚‰ãã“ã®æ–‡ç« ã‚’èªã‚“ã§ã„ã‚‹ã»ã¨ã‚“ã©ã®äººã¨åŒæ§˜ã« Haskell ã®å‹‰å¼·ã‚’ã—ãŸã“ã¨ãŒãã£ã‹ã‘ã§ã—ãŸã€‚ Haskell ã®ãƒ¢ãƒŠãƒ‰ãªã©ã‚’åˆ©ç”¨ã™ã‚‹ä¸Šã§ã¯åœè«–ã‚’ç†è§£ã™ã‚‹å¿…è¦ã¯å…¨ããªã„ã®ã§ã™ãŒã€åž‹ã‚·ã‚¹ãƒ†ãƒ ã‚„å‡¦ç†ç³»ã«é–¢ã—ã¦è©³ã—ãçŸ¥ã‚ŠãŸãã¦è«–æ–‡ã‚’èªã‚€ã¨åœè«–ã®è¨€è‘‰ãŒæ™®é€šã«ä½¿ã‚ã‚Œã¦ã„ã¦ã€ç†è§£ã§ããšã«æ–å¿µã—ã¦ã„ã¾ã—ãŸã€‚ ãã“ã§ã€å½“æ™‚æ•°äººãŒé›†ã¾ã£ã¦ã‚„ã£ã¦ã„ãŸåœè«–å‹‰å¼·ä¼šã«å‚åŠ ã—ã¦åœè«–ã®å‹‰å¼·ã‚’å§‹ã‚ã¾ã—ãŸã€‚å½“æ™‚èªã‚“ã§ã„ãŸæ›¸ç±ã¯ Conceptual Mathematics: A First Introduction to Categories ã§ã—ãŸã€‚ã“ã®æœ¬ã¯åœè«–ã®åˆå¦è€…å‘ã‘ã«æ›¸ã‹ã‚ŒãŸæœ¬ã§ã€æ•°å¦çš„ãªçŸ¥è˜ã‚’ã»ã¨ã‚“ã©ä»®å®šã›ãšã«ç†è§£ã§ãã‚‹ã‚ˆã†ã«æ›¸ã‹ã‚Œ
notae 2016/01/20
Category
ãƒªãƒ³ã‚¯
String diagram ã®ã™ã™ã‚ - PS
ã“ã¡ã‚‰ã¯ Haskell Advent Calendar 2015 - Qiita ã® 20 æ—¥ç›®ã®è¨˜äº‹ã§ã™ã€‚ å‰ã®æ—¥ï½¥ï½¥ï½¥Hakyllã§ãƒ–ãƒã‚°ã‚’ä½œã‚‹(å®Ÿè·µç·¨) - Wake up! Good night* æ¬¡ã®æ—¥ï½¥ï½¥ï½¥ã€Œç¬¬2æœŸ Hæœ¬èªæ›¸ä¼š in ç§‹è‘‰åŽŸã€ã‚’çµ‚ãˆã¦ #readhbon #haskell - ã‚»ã‚«ã‚¤ãƒŽã‚«ã‚¿ãƒ String diagram String diagram ã¨ã„ã†ã®ã¯ åœè«–ã® bicategory ã¨ã„ã†ã®ã‚’ã€å¹³é¢ä¸Šã®ç‚¹ã¨ç·šã‚’ä½¿ã£ã¦æãã‚‚ã®ãªã‚“ã§ã™ãŒã€ç‰¹ã«ã‚„ã‚„ã“ã—ã„çŸ¥è˜ãŒç„¡ãã¦ã‚‚ä½¿ãˆã‚‹(ä½¿ã£ã¦ã„ã‚‹)ã€ã¨æ€ã£ãŸã®ã§è¨˜äº‹ã«ã—ã¾ã—ãŸã€‚ ä»¥ä¸‹ã€åœè«–ã®çŸ¥è˜ã¯å¿…è¦ã‚ã‚Šã¾ã›ã‚“ã€‚ åž‚ç›´æ–¹å‘ã«ã¤ã„ã¦ åž‹ã‚’ç¸¦ç·šã§è¡¨ç¾ã—ã€é–¢æ•°ã¯ç¸¦ç·šä¸Šã®ãƒŽãƒ¼ãƒ‰ã§è¡¨ç¾ã—ã¾ã™: è«¸èˆ¬ã®äº‹æƒ…ã§å››è§’ã«ãªã£ã¦ã¾ã™ãŒã€ãƒŽãƒ¼ãƒˆã«æ›¸ãã¨ãã¯ä¸¸ã§ã‚‚ä½•ã§ã‚‚ã‹ã¾ã„ã¾ã›ã‚“ã€‚ å®šç¾©åŸŸaãŒä¸‹ã«ãªã£ã¦ã„ã‚‹ã“ã¨ã«æ³¨æ„ã€‚ é–¢æ•°id = \
notae 2015/12/31
Category
ãƒªãƒ³ã‚¯
Categories for the Working Mathematician
Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transf ormation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphism
notae 2015/12/30
Category

Math
ãƒªãƒ³ã‚¯
From Lenses to Yoneda Embedding
From Lenses to YonedaÂ Embedding Posted by Bartosz Milewski under Category Theory, Functional Programming, Haskell, Lens, Programming [6] Comments Lenses are a fascinating subject. Edward Kmettâ€™s lens library is an indispensable tool in every Haskell programmerâ€™s toolbox. I set out to write this blog post with the goal of describing some new insights into their categorical interpretation, but then
notae 2015/08/04
Haskell

Lens

Category
ãƒªãƒ³ã‚¯
åœè«–ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžCPLå…¥é–€ - ã†ã•ãŽå°å±‹
é¢ç™½ã‹ã£ãŸã®ã§å…¥é–€è¨˜äº‹ã‚’æ›¸ãã¾ã—ãŸã€‚haskellã®çŸ¥è˜ã‚’ä»®å®šã—ã¾ã™ãŒåœè«–ã®çŸ¥è˜ã¯ä¸€åˆ‡è¦æ±‚ã—ã¾ã›ã‚“ã€‚ è¨€èªžæ¦‚è¦ åœè«–ã«åŸºã¥ã ãƒ‡ãƒ¼ã‚¿ã¯å°„ã¨ã—ã¦è¡¨ã™ é–¢æ•°ã¯å°„ã‚ã‚‹ã„ã¯ç¾ƒå¯¾è±¡ã¨ã—ã¦è¡¨ã™ Turingå®Œå…¨ã§ãªã„ è¨ˆç®—ã¯å¿…ãšåœæ¢ã™ã‚‹ ä½œè€…ã¯æ—¥æœ¬äºº ç’°å¢ƒå°Žå…¥ haskellã«ã‚ˆã‚‹å®Ÿè£…ãŒå˜åœ¨ã™ã‚‹ã®ã§ã“ã‚Œã‚’ç”¨ã„ã¾ã™ã€‚cabalã‚’ç”¨ã„ã¦ä»¥ä¸‹ã§ã™ã¹ã¦æ¸ˆã¿ã¾ã™ã€‚ 1 $ cabal install CPL èµ·å‹•ã™ã‚‹ã«ã¯cplã¨å©ãã¾ã™ã€‚ 1 2 3 4 5 6 7 $ cpl Categorical Programming Language (Haskell version) version 0.0.7 Type help for help cpl> å¼•æ•°ã«ãƒ•ã‚¡ã‚¤ãƒ«ã‚’ä¸Žãˆã‚‹ã¨ãã‚Œã‚’å®Ÿè¡Œã—ã¾ã™ã€‚ä¸èº«ã‚’æ¨™æº–å…¥åŠ›ã‹ã‚‰æµã—ã“ã‚“ã ã‹ã®ã‚ˆã†ãªã‹ã®æŒ™å‹•ã‚’ã—ã¾ã™ã€‚èªã¿è¾¼ã‚“ã å¾Œreplã«å…¥ã‚‹ã‚ªãƒ—ã‚·ãƒ§ãƒ³-iã‚‚ã‚ã‚Šã¾ã™ã€‚ 1 $
notae 2015/07/10
Category
ãƒªãƒ³ã‚¯
Category Theory (Oxford Logic Guides)
OXFORD LOGIC GUIDES Series Editors A.J. MACINTYRE D.S. SCOTT Emeritus Editors D.M. Gabbay John Shepherdson OXFORD LOGIC GUIDES For a full list of titles please visit http://www.oup.co.uk/academic/science/maths/series/OLG/ 21. C. McLarty: Elementary categories, elementary toposes 22. R.M. Smullyan: Recursion theory for metamathematics 23. Peter Clote and Jan KrajÂ´Ä±cek: Arithmetic, proof theory, an
notae 2015/06/19
Category

Math
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Lensã§è¡Œã“ã†ï¼(2):Isoã¸ã®æ‹¡å¼µ - Just $ A sandbox
ã“ã®ã‚¨ãƒ³ãƒˆãƒªãƒ¼ã¯Lensã§è¡Œã“ã†ï¼ - ã¿ã‚‡ã‚“ã•ã‚“ã®ã€‚ã®ç¶šç·¨ã«ã‚ãŸã‚Šã¾ã™ã€‚ å‰å›žã®å¾©ç¿’ å‰å›žã€Lensåž‹ã«ã¤ã„ã¦è©³ã—ãè¦‹ã¾ã—ãŸã€‚ Lensåž‹ã¯ä»¥ä¸‹ã®ã‚ˆã†ãªåž‹ã®ãƒ‡ãƒ¼ã‚¿ã§ã™ã€‚ type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t ã“ã‚Œã¯Fuctorã‚’ä¸Šæ‰‹ãå®šã‚ã¦ã‚„ã‚Œã°(Constã¨Identityã§ã—ãŸãï¼)getter,setterã¨ã—ã¦æŒ¯ã‚‹èˆžã†ã“ã¨ã®ã§ãã‚‹ç´ æ•µãªåž‹ã§ã—ãŸã€‚ ã•ã¦ã€ã“ã®åž‹ãŒã©ã‚Œã ã‘ã®åŠ›ã‚’æŒã£ã¦ã„ã‚‹ã‹ã‚’å®Ÿæ„Ÿã—ãŸæ–¹ã¯ã€ãã£ã¨ã€Œã“ã‚“ãªã‚„ã‚„ã“ã—ãã†ã«è¦‹ãˆã‚‹åž‹ãŒã©ã“ã‹ã‚‰é™ã£ã¦ããŸã®ã‹ï¼Ÿã€ã¨ã„ã†ç–‘å•ãŒæ¹§ã„ã¦ãã‚‹ã¨æ€ã„ã¾ã™ã€‚ ä»Šå›žã¯ã“ã®ã“ã¨ã«ã¤ã„ã¦è¦‹ã¦ã„ãã“ã¨ã«ã—ã¾ã™ã€‚ Isoåž‹ã¨ã¯ï¼Ÿ ã§ã¯Lensã«ã¤ã„ã¦è€ƒãˆã‚‹ã®ã«ã€ã‚„ã¯ã‚ŠHackageã‚’å‚ç…§ã—ã¾ã—ã‚‡ã†â†’The lens package ã“ã®ãƒšãƒ¼ã‚¸çœŸã‚“ä¸ã«ã€å¤§ã
notae 2015/05/08
Haskell

Lens

Category
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Arrows: A General Interface to Computation
Arrows are a new abstract view of computation, defined by John Hughes [Hug00]. They serve much the same purpose as monads -- providing a common structure for libraries -- but are more general. In particular they allow notions of computation that may be partially static (independent of the input) or may take multiple inputs. If your application works fine with monads, you might as well stick with t
notae 2015/04/16
Haskell

Category

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åœè«–å‹‰å¼·ä¼š @ ãƒ¯ãƒ¼ã‚¯ã‚¹ã‚¢ãƒ—ãƒªã‚±ãƒ¼ã‚·ãƒ§ãƒ³ã‚º
Seminar of category theory
notae 2015/02/09
Category
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Natural Transformations in Haskell - Quickstart - Open wiki - Gitorious
Examples and answers for the "Natural Transf ormations in Haskell" workshop first given at Compose Conference. Prerequisites GHC 7.8.* or later cabal 1.18 or later your Haskell editor bzr or git the below project built with cabal build; basic instructions below Check out the project You can choose either bzr or git to get the project on your machine. bzr bzr branch lp:nt-in-haskell git git clone h
notae 2015/02/02
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Haskell

Category
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CPL
CPL: An interpreter of Hagino's Categorical Programming Language (CPL). CPL is a functional programming language based on category theory. Data types are declared in a categorical manner by adjunctions. Data types that can be handled include the terminal object, the initial object, the binary product functor, the binary coproduct functor, the exponential functor, the natural number object, the fun
notae 2015/01/21
Haskell

Category
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Introduction to Categorical Programming (Revised)
Masahiro Sakai's presentation at HAMA.jp <http: />. (revised version)Read less
notae 2015/01/09
Haskell

Category
ãƒªãƒ³ã‚¯
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