Programming Language Foundations in Agda – Table of Contents
This book is an introduction to programming language theory using the proof assistant Agda. Comments on all matters—organisation, material to add, material to remove, parts that require better explanation, good exercises, errors, and typos—are welcome. The book repository is on GitHub. Pull requests are encouraged. There is a private repository of answers to selected questions on github. Please co
Codensity Monad - Just $ A sandbox
Codensity ã¨ã„ã†åž‹ãŒã‚ã‚‹. 定義ã¯ä»¥ä¸‹. newtype Codensity m a = Codensity { runCodensity :: forall b. (a -> m b) -> m b } instance Functor (Codensity k) where fmap f (Codensity m) = Codensity (\k -> m (k . f)) instance Monad (Codensity f) where return x = Codensity (\k -> k x) m >>= k = Codensity (\c -> runCodensity m (\a -> runCodensity (k a) c)) ã“ã‚Œã®ä½•ãŒè‰¯ã„ã‹ã¨è¨€ã†ã¨, ã“ã‚Œã¯ä»¥ä¸‹ã®ã‚ˆã†ã«MonadFreeãªä½œç”¨ã‚’æŒã¤. instance (Functor f, Mon
Become a Better Haskeller by Learning About Inductive Types | Marko Dimjašević
Posted on April 8, 2019 by Marko Dimjašević In the functional programming world, we rely on languages with type systems that help us write, extend and maintain our software. These type systems, such as the one in Haskell, are based on solid type theory. While we usually and easily see the benefits of having a static type system on simple types such as integers, we might fail to see the benefits of
定ç†è¨¼æ˜Žæ”¯æ´ã®ç´¹ä»‹ - Qiita
目的 定ç†è¨¼æ˜Žæ”¯æ´ã¨ã¯ä½•ã‹ã¨ç¾çŠ¶ã®æ•´ç†ã€‚ 定ç†è¨¼æ˜Žæ”¯æ´ã¨ã¯ 定ç†è¨¼æ˜Žæ”¯æ´ã¨ã¯æ•°å¦ã®å®šç†ã‚’自動ã§è¨¼æ˜Žã™ã‚‹ã“ã¨ã§ã¯ãªãã€ã‚¹ãƒ†ãƒƒãƒ—ãƒã‚¤ã‚¹ãƒ†ãƒƒãƒ—ã§ã‚³ãƒ³ãƒ”ュータã«å‘½ä»¤ã‚’é€ã‚Šã€æ•°å¦ã®å®šç†ã‚’証明ã™ã‚‹ã®ã‚’助ã‘るシステムã§ã‚る。 支æ´ã ã‹ã‚‰æ„味ãªã„ã¨ã„ã†ã“ã¨ã§ãªãã€æœ€è¿‘ã®æ•°å¦ã®è¨¼æ˜Žã¯é•·ããªã‚Šè¨¼æ˜Žã®æ¤œè¨¼ãŒé›£ã—ã„ã®ã‚’助ã‘ã‚‹æ„味ãŒã‚る。定ç†è¨¼æ˜Žæ”¯æ´ã®æ„義ã«ã¤ã„ã¦ã¯ã“ã¡ã‚‰ãŒè©³ã—ã„。 ã¾ãŸã€ä¿¡é ¼æ€§ãŒæ±‚ã‚らる難ã—ã„アルゴリズムã®æ¤œè¨¼ã€ãŸã¨ãˆã°TLS(æš—å·é€šä¿¡)ã‚„Raft(分散åˆæ„アルゴリズム)ã®ã‚µãƒ¼ãƒãƒ¼ã«åˆ©ç”¨ã•ã‚Œã¤ã¤ã‚る。 ã“ã“ã§ã„ã†å®šç†ã¯å¤§ã’ã•ãªã‚‚ã®ã ã‘ã§ãªãã€$1+1=2$ã€$0何ã‹=0$ã€$ab=b*a$ã¨ã„ã£ãŸç°¡å˜ãªã‚‚ã®ã‚’証明ã—ãªãŒã‚‰ã©ã‚“ã©ã‚“ç©ã¿ä¸Šã’ã¦ã„ã。通常ã®ãƒ—ãƒã‚°ãƒ©ãƒ ã¨é•ã†ã®ã¯è¨¼æ˜Žã§ã‚ã‚‹ã®ã§ä½¿ç”¨ã™ã‚‹å¤‰æ•°ãŒæ•´æ•°ãªã‚‰ãã®ã™ã¹ã¦ã®å€¤ã«ã¤ã„ã¦æˆã‚Šç«‹ã¤å®šç†ã‚’証明ã™ã‚‹ã€‚ 定ç†ã‚’証明ã™ã‚‹ã®ã«ä½¿ã†ãƒ„ールã¯ä¸‹è¨˜ã§ã‚る。(ä»–
Agda ãƒãƒ³ã‚ºã‚ªãƒ³æ´»å‹•å ±å‘Š
ã“ã‚“ã«ã¡ã¯ã€@trigottã§ã™ã€‚ã“ã®è¨˜äº‹ã§ã¯ã€ç¤¾å†…ã§è¡Œã£ã¦ã„ã‚‹ Agda ãƒãƒ³ã‚ºã‚ªãƒ³ã®ç´¹ä»‹ã‚’ã—ã¾ã™ã€‚ ã¯ã˜ã‚ã« Agda ã¨ã¯ã€ä¾å˜åž‹ã®ä½¿ãˆã‚‹é–¢æ•°åž‹ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžã€ã‚ã‚‹ã„ã¯å®šç†è¨¼æ˜Žæ”¯æ´ç³»ã§ã™ã€‚Coq ãªã©ã¨ã¯é•ã„タクティックã¯ä½¿ã‚ãšè¨¼æ˜Žé …を直接記述ã™ã‚‹ã‚¹ã‚¿ã‚¤ãƒ«ã§ã™ãŒã€Emacs 上ã§å¯¾è©±çš„ã«è¨¼æ˜Žã‚’進ã‚ã‚‹ãŸã‚ã®ã‚¤ãƒ³ã‚¿ãƒ•ã‚§ãƒ¼ã‚¹ãŒç”¨æ„ã•ã‚Œã¦ã„ã‚‹ãŸã‚ã€åŠ¹çŽ‡çš„ã«è¨¼æ˜Žã‚’進ã‚ã‚‹ã“ã¨ãŒã§ãã¾ã™ã€‚Agda 㧠n * 2 㨠n + n ãŒç‰ã—ã„ã“ã¨ã‚’証明ã™ã‚‹å‹•ç”»ã‚’撮影ã—ã¦ã¿ã¾ã—ãŸã€‚雰囲気ãŒã¤ã‹ã‚ã‚Œã°å¹¸ã„ã§ã™ã€‚ KLab ã§ã¯æœˆã«ï¼‘回 ALM(All Layers Meeting)ã¨ã„ã†ç¤¾å†…勉強会を開催ã—ã¦ã„ã¾ã™ã€‚å¦ç”Ÿã®ã“ã‚ã‹ã‚‰ Agda ãŒå¥½ãã§è§¦ã£ã¦ã„ãŸã“ã¨ã‚‚ã‚ã£ã¦ã€Agda ã«é–¢ã™ã‚‹ç™ºè¡¨ã‚’ã—ãŸã¨ã“ã‚ã€å…ˆè¼©ã‹ã‚‰ãƒãƒ³ã‚ºã‚ªãƒ³ã‚’é–‹ã„ã¦ã»ã—ã„ã¨ã„ã†ã“ã¨ã‚’言ã‚ã‚Œã¾ã—ãŸã€‚ãƒãƒ³ã‚ºã‚ªãƒ³ã¨ã‹ã‚„ã£ãŸã“ã¨ãªã„ã—ã€Agd
実世界を扱ã†ä¾å˜åž‹ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°ã®ãŸã¶ã‚“基本～外界ã‹ã‚‰å®‰å…¨ãªä¸–ç•Œã¾ã§ã®é“ - ã¼ãã®ã¬ã¾ã¡ 出張版
ä¾å˜åž‹ãªã‚‰ã•ã‚‰ã«å®‰å…¨ã«ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°ã§ãã¡ã¾ã†ã‚“ã ï¼ã¨è¨€ã£ãŸã¨ã“ã‚ã§ï¼Œã€Œç„¡æ–™ã§éŠã¹ã¡ã¾ã†ã‚“ã ï¼ã€ã¨ã‹ã€Œ3000円払ãˆã°ç„¡æ–™ã§10連ã¾ã‚ã›ã‚‹ã€ã¿ãŸã„ãªæ„ŸãŒã‚り， ä¾å˜åž‹ä½¿ã‚ãªã„å ´åˆã¨ã©ã†é•ã£ã¦ãã‚‹ã®ã‹ 入出力ã‹ã‚‰æ‰±ã„始ã‚ã‚‹ã¨ã©ã†ã„ã£ãŸå½¢ã®ãƒ—ãƒã‚°ãƒ©ãƒ ã«ãªã‚‹ã®ã‹ 大概ã©ã†ã„ã†æµã‚Œã§ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°ã™ã‚‹ã“ã¨ã«ãªã‚‹ã®ã‹ ã¨ã‹ï¼Œãã†ã„ã£ãŸè©±ã‚’通ã—ã§ã¯ãã‚“ãªã«è¦‹ãªã„ã‹ãªãƒ¼ã¨ã„ã†æ°—ãŒã—ãŸã®ã§ï¼Œã”ã基本的ãªã‚‚ã®ã‚’一通りã¾ã¨ã‚ã¦ãŠã“ã†ã¨æ€ã£ã¦ï¼Ž ã¾ãšï¼Œèª¬æ˜Žã«ä½¿ã†å•é¡Œè¨å®šã«ã¤ã„ã¦ï¼Žè¡Œåˆ—演算，特ã«è¡Œåˆ—ç©ã‚’考ãˆã¦ã¿ã‚‹ï¼ŽãŸã ã—，行列ã®å½¢(è¡Œã¯ã„ãã¤ï¼Œåˆ—ã¯ã„ãã¤)ã«ã¤ã„ã¦ã¯ãƒ—ãƒã‚°ãƒ©ãƒ ã®å¤–ã‹ã‚‰å…¥åŠ›ã«ã‚ˆã£ã¦æ±ºå®šã™ã‚‹ã‚ˆã†ãªçŠ¶æ³ã¨ã™ã‚‹ï¼Žã“れ自体ã¯æ™®é€šã®å•é¡Œè¨å®šã ã¨æ€ã‚れる． ä¾å˜åž‹ã‚’使ã‚ãªã‘ã‚Œã°ç‰¹ã«ã©ã†ã¨ã„ã†ã“ã¨ã‚‚ç„¡ã„．æらã行列ã®åž‹ã‚’次ã®ã‚ˆã†ã«å®šç¾©ã—， -- å½¢ã®ã¿æŒã£ã¦ãŠã，ä¸èº«ã®æ•°å€¤ã«ã¤ã„ã¦ã¯ç°¡å˜ã®ãŸã‚çœç•¥ data Ma
安全ã‹ã¤æŸ”軟ãªä¾å˜åž‹ -
ã“ã®è¨˜äº‹ã¯Theorem Proving Advent Calendar 2011ã®1日目ã®è¨˜äº‹ã§ã™ã€‚ 今日㯠Agda2 ã¨ã„ã†ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžã‚’用ã„ã¦ã€ä¾å˜åž‹ã‚’用ã„ã‚‹ã“ã¨ã§çµ¶å¯¾çš„ãªå®‰å…¨æ€§ã¨ Haskell ã‚„ OCaml ãªã©ã§ã¯(通常ã®æ–¹æ³•ã§ã¯)実ç¾ã§ããªã„柔軟ã•ã®ã©ã¡ã‚‰ã‚‚æŒã¤ãƒ—ãƒã‚°ãƒ©ãƒ を記述ã§ãã‚‹ã¨ã„ã†ã“ã¨ã«ã¤ã„ã¦æ›¸ãã¾ã™ã€‚ ã“ã®è¨˜äº‹ã¯ä¸»ã«ã€æ™®æ®µå‹•çš„型付ã‘ã®ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžã‚’使ã£ã¦ã„ã¦ã€é™çš„型付ãã®è¨€èªžã§ã¯è‡ªåˆ†ã®æ„図ã—ãŸã‚‚ã®ã‚’å分ã«è¡¨ç¾ã§ããªã„ã¨è€ƒãˆã¦ã„る人を対象èªè€…ã¨ã—ã¦ã„ã¾ã™ã€‚ ä¾å˜åž‹ã¨ã¯ åž‹ã«ä¾å˜ã™ã‚‹åž‹ã‚„ã€å€¤ã«ä¾å˜ã™ã‚‹åž‹ã‚’作れる型ã®ã“ã¨ã§ã™ã€‚ 例ãˆã°ã€å€¤ã«ä¾å˜ã™ã‚‹åž‹ã‚’用ã„ã‚‹ã“ã¨ã§åž‹ãƒ¬ãƒ™ãƒ«ã§ã‚µã‚¤ã‚ºãŒä¸Žãˆã‚‰ã‚Œã¦ã„るリストを作るã“ã¨ãŒå¯èƒ½ã§ã™ã€‚ ã¾ãŸã€ãƒªã‚¹ãƒˆã®çµåˆé–¢æ•°ã¯é•·ã• a ã®ãƒªã‚¹ãƒˆã¨é•·ã• b ã®ãƒªã‚¹ãƒˆã‚’å–ã‚Šã€ãƒªã‚¹ãƒˆ a+b ã®ãƒªã‚¹ãƒˆã‚’è¿”ã™ã¨ã„ã†ã‚ˆã†ãªåž‹ã‚’æŒã¤ã“ã¨ã«ãªã‚Šã¾ã™
1
ランã‚ング
ãŠçŸ¥ã‚‰ã›
ランã‚ング
リリースã€éšœå®³æƒ…å ±ãªã©ã®ã‚µãƒ¼ãƒ“スã®ãŠçŸ¥ã‚‰ã›
最新ã®äººæ°—エントリーã®é…ä¿¡
j次ã®ãƒ–ックマーク
kå‰ã®ãƒ–ックマーク
lã‚ã¨ã§èªã‚€
eコメント一覧を開ã
oページを開ã
Pipelining in TypedProtocols
GitHub - andreasabel/agda2lagda: Simple conversion from Agda text to literate Agda text.
https://dl.acm.org/doi/book/10.1145/2841316
Quantifiers in Agda
GitHub - plum-umd/cgc: Constructive Galois connections
GitHub - notogawa/agda-haskell-example: example haskell project with agda code generation
{{#tags}}- {{label}}
{{/tags}}