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# HG changeset patch # User Shinji KONO # Date 1389401312 -32400 # Node ID 5b51dffd2b19e7c15933a7fb854d7fc84ff8d755 # Parent 0a2454365e558765483ec28408dc5122c78a574b add fig diff -r 0a2454365e55 -r 5b51dffd2b19 presen/agda-prog.ind --- a/presen/agda-prog.ind Sat Jan 11 00:52:00 2014 +0900 +++ b/presen/agda-prog.ind Sat Jan 11 09:48:32 2014 +0900 @@ -1,6 +1,6 @@ -title: Agda での Programming 技術 --author: 河野真治 +-author: 　 --なんで、今、証明支援系なのか? @@ -8,8 +8,17 @@ Haskell が流行ってるようだが… + Haskell はMonad使いまくり + Monadって何? +--この発表は... + +Agdaをさんざん触って面白かった + + 1部　Monad って何? + 2部　Agda って何? + --Monadって何? Monad を解説しているサイトは多いが、多くは皮相的 @@ -18,7 +27,7 @@ →　だったら、Monad を証明支援系を使って理解すれば良いんじゃないの? -とりあえず、目標は Monad の合成則 +とりあえず、目標は Monad の合成則の証明 --圏 @@ -37,7 +46,12 @@ これだけ。(あとは、Functor, Natural Transformation, Adjunction, Monad ... ) ---圏と関数型プログラミング +--射と合成則 + +

+ + +--圏と関数型プログラミングとの関係射が関数 ( = 関数型プログラミングのプログラム) @@ -53,19 +67,26 @@ 型は圏でもある。 + Int → List + --Functor -Functor F とは、Category C から D への写像 -対象AをDの対象B対応させる写像をFObjとする。 +Functor F とは、Category C から D への射 + +Cの対象aをDの対象a'に対応させる写像をFObjとする。 +Cの射fをDの射f'に対応させる写像をFMapとする。 + 射の対応が、以下を満たす時に、F はFunctor と言う。 - (1) C の射 f:A->B を Dの射 F(f):F(A)->F(B) に割り当てる (FMap) - (2) id(F(A)) = F(id(A)) - (3) f: A->B, g: B->C に対して、 - F(g) ○ F(f) : F(g○f) + (1) C の射 f:a->b を Dの射 F(f):F(a)->F(b) に割り当てる (FMap) + (2) id(F(a)) = F(id(a)) + (3) f: a->b, g: b->c に対して、 + F(g) ○ F(f) : F(g○f) 分配法則 Functor は対象の写像FObjと、射の写像FMapの二つを持つ。 +Functor の数学記法は polymorphic + --Constructor としての Functor Integer と List はどちらも圏であり、 @@ -81,10 +102,11 @@ | Leaf a List や Node を Functor のFObj(対象の射)として考えることができる。 +(Leaf や :: は　constructor ) --FMap -Functor は射の写像も持っている必要があり、fmap として(自分で)定義する。 +Functor の射の写像は、fmap として(自分で)定義する。 class Functor f where fmap :: (a->b) -> f a -> f b @@ -177,8 +199,24 @@

-合成則の証明は煩雑 +合成則の証明は +煩雑 + +--Haskell 使うのに圏論とか必要なのか? + +知らなくても困らない + +Monad とか用語は理解できる +Functor と map はわかる + +煩雑な証明を自分でやって理解する + +そもそも証明自体が圏論( Curry Howard 対応) + +Curry Howard 対応な証明支援系である Agda を使えば? + +(これで1部終わり。長かった...) --Curry Howard 対応 @@ -461,9 +499,28 @@ --結局、Monad は役に立つのか? +メタプログラミング(IOや並列処理)として便利 + +構文やややうざい。C のプログラミングみたい。 + +結合則や Functor(fmapを持つ) は必須ではない + +Monad の合成はさらに煩雑 (Beck Law) + +Monad Transform も「一度Monadを分解して再合成」 + +圏論知らなくても使えるが、勉強すれば用語は納得できる --結局、証明は役に立つのか? +Monad に関しては役に立たない + +圏論を理解するのは役に立つ + +教科書は「道標のみ」 + +自分で山を登らないと。山を登るためのツール。 + --Agda は面白い詰将棋みたいなもの @@ -472,7 +529,16 @@ Agda は Coq よりもマイナー +Agda の情報が少ないので面白い +みんな Agda を使おう! +--おまけ + +Agda は Emacs で使うもの + +Vimmer にはつらすぎる (手がつる) + +vim emulator を使うと幸せになれます diff -r 0a2454365e55 -r 5b51dffd2b19 presen/fig/Kleisli.graffle --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/presen/fig/Kleisli.graffle Sat Jan 11 09:48:32 2014 +0900 @@ -0,0 +1,373 @@ + + + + + ActiveLayerIndex + 0 + ApplicationVersion + + 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